Hypothesis Testing for Population Proportions Explained

12/9/23, 10:06 PM Chapter 9 Hypothesis Tests for a Single Population Proportion (counts towards your grade) https://egcc.instructure.com/courses/40375/assignments/1211620?module_item_id=3857931 1/16 1/1 pt Details Question 2 1/1 pt Details left-tailed right-tailed two-tailed Test the claim that the proportion of men who own cats is significantly different than 70% at the 0.02 significance level. The null and alternative hypothesis would be: The test is: Based on a sample of 25 people, 76% owned cats The test statistic is: .65 (to 2 decimals) The positive critical value is: 2.33 (to 2 decimals) Based on this we: Reject the null hypothesis Fail to reject the null hypothesis Question Help: Message instructor Test the claim that the proportion of people who own cats is larger than 80% at the 0.025 significance level. The null and alternative hypothesis would be:

12/9/23, 10:06 PM Chapter 9 Hypothesis Tests for a Single Population Proportion (counts towards your grade) https://egcc.instructure.com/courses/40375/assignments/1211620?module_item_id=3857931 2/16 The test is: left-tailed right-tailed two-tailed Based on a sample of 700 people, 82% owned cats The test statistic is: 1.32 (Round to 2 decimals ) The p-value is: .09 (Round to 2 decimals ) Based on this we: Reject the null hypothesis

12/9/23, 10:06 PM Chapter 9 Hypothesis Tests for a Single Population Proportion (counts towards your grade) https://egcc.instructure.com/courses/40375/assignments/1211620?module_item_id=3857931 3/16 Question 3 1/1 pt Details Do not reject the null hypothesis Question Help: Message instructor left-tailed two-tailed right-tailed A well-known brokerage firm executive claimed that 80% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that in a sample of 400 people, 87% of them said they are confident of meeting their goals. Test the claim that the proportion of people who are confident is larger than 80% at the 0.01 significance level. The null and alternative hypothesis would be: The test is: The test statistic is: 3.5 (to 3 decimals) The p-value is: .0002 (to 4 decimals) Based on this we: Reject the null hypothesis Fail to reject the null hypothesis Question Help: Message instructor

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

12/9/23, 10:06 PM Chapter 9 Hypothesis Tests for a Single Population Proportion (counts towards your grade) https://egcc.instructure.com/courses/40375/assignments/1211620?module_item_id=3857931 4/16 Question 4 1/1 pt Details A recent newspaper article claims that 54% of car accidents involve some evidence of distracted driving. A police officer questions this claim, and pulls a random sample of 95 accident reports. If 43 of them involve distracted driving, is this enough evidence to show that the proportion of car accidents involve some evidence of distracted driving is significantly different from than reported by the newspaper? (Use =0.025) 1. For this study, we should use 2. The null and alternative hypotheses would be: : .54 (please enter a decimal) : .54 (Please enter a decimal) 3. The test statistic = -1.709 (please show your answer to 3 decimal places.) 4. The p-value = .0875 (Please show your answer to 4 decimal places.) 5. The p-value is Hypothesis Test for a Population Proportion p = p ≠ >

12/9/23, 10:06 PM Chapter 9 Hypothesis Tests for a Single Population Proportion (counts towards your grade) https://egcc.instructure.com/courses/40375/assignments/1211620?module_item_id=3857931 5/16 Question 5 1/1 pt Details 6. Based on this, we should the null hypothesis. 7. As such, the final conclusion is that ... The sample data suggest that the populaton proportion is significantly different from 54% at = 0.025, so there is sufficient evidence to conclude that the proportion of car accidents involve some evidence of distracted driving is different from 54% The sample data suggest that the population proportion is not significantly different from 54% at = 0.025, so there is not sufficient evidence to conclude that the proportion of car accidents involve some evidence of distracted driving is different from 54%. Question Help: fail to reject Message instructor You are conducting a study to see if the proportion of voters who prefer Candidate A is significantly larger than 67% at a significance level of = 0.05. According to your sample, 75 out of 100 potential voters prefer Candidate A. 1. For this study, we should use 2. The null and alternative hypotheses would be: : .67 (please enter a decimal) : .67 (Please enter a decimal) Hypothesis Test for a Population Proportion p = p >

12/9/23, 10:06 PM Chapter 9 Hypothesis Tests for a Single Population Proportion (counts towards your grade) https://egcc.instructure.com/courses/40375/assignments/1211620?module_item_id=3857931 6/16 Question 6 1/1 pt Details 3. The test statistic = 1.701 (please show your answer to 3 decimal places.) 4. The p-value = 0.0445 (Please show your answer to 4 decimal places.) 5. The p-value is 6. Based on this, we should the null hypothesis. 7. As such, the final conclusion is that ... The sample data suggest that the population proportion is not significantly larger than 67% at = 0.05, so there is not sufficient evidence to conclude that the proportion of voters who prefer Candidate A is larger than 67%. The sample data suggest that the populaton proportion is significantly larger than 67% at = 0.05, so there is sufficient evidence to conclude that the proportion of voters who prefer Candidate A is larger than 67% Question Help: less than (or equal to) reject Message instructor In a certain school district, it was observed that 30% of the students in the element schools were classified as only children (no siblings). However, in the special program for talented and gifted children, 137 out of 409 students are only children. The school district administrators want to know if the proportion of only children in the special program is significantly different from the proportion for the school district. Test at the level of significance. What is the hypothesized population proportion for this test?

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

12/9/23, 10:06 PM Chapter 9 Hypothesis Tests for a Single Population Proportion (counts towards your grade) https://egcc.instructure.com/courses/40375/assignments/1211620?module_item_id=3857931 7/16 (A) (B) (C) (D) (E) (F) .30 (Report answer as a decimal accurate to 2 decimal places. Do not report using the percent symbol.) Based on the statement of this problem, how many tails would this hypothesis test have? one-tailed test two-tailed test Choose the correct pair of hypotheses for this situation: (A) (B) (C) (D) (E) (F) Using the normal approximation for the binomial distribution (without the continuity correction), what is the test statistic for this sample based on the sample proportion? 1.543 (Report answer as a decimal accurate to 3 decimal places.) You are now ready to calculate the P-value for this sample. P-value = 0.1228 (Report answer as a decimal accurate to 4 decimal places.) This P-value (and test statistic) leads to a decision to... reject the null accept the null fail to reject the null reject the alternative

12/9/23, 10:06 PM Chapter 9 Hypothesis Tests for a Single Population Proportion (counts towards your grade) https://egcc.instructure.com/courses/40375/assignments/1211620?module_item_id=3857931 8/16 Question 7 1/1 pt Details As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the assertion that there is a different proportion of only children in the G&T program. There is not sufficient evidence to warrant rejection of the assertion that there is a different proportion of only children in the G&T program. The sample data support the assertion that there is a different proportion of only children in the G&T program. There is not sufficient sample evidence to support the assertion that there is a different proportion of only children in the G&T program. Question Help: Message instructor In a certain school district, it was observed that 32% of the students in the element schools were classified as only children (no siblings). However, in the special program for talented and gifted children, 152 out of 388 students are only children. The school district administrators want to know if the proportion of only children in the special program is significantly different from the proportion for the school district. Test at the level of significance. What is the hypothesized population proportion for this test? .32 (Report answer as a decimal accurate to 2 decimal places. Do not report using the percent symbol.) Based on the statement of this problem, how many tails would this hypothesis test have? one-tailed test two-tailed test

12/9/23, 10:06 PM Chapter 9 Hypothesis Tests for a Single Population Proportion (counts towards your grade) https://egcc.instructure.com/courses/40375/assignments/1211620?module_item_id=3857931 9/16 (A) (B) (C) (D) (E) (F) Choose the correct pair of hypotheses for this situation: (A) (B) (C) (D) (E) (F) Using the normal approximation for the binomial distribution (without the continuity correction), was is the test statistic for this sample based on the sample proportion? 3.030 (Report answer as a decimal accurate to 3 decimal places.) You are now ready to calculate the P-value for this sample. P-value = .0024 (Report answer as a decimal accurate to 4 decimal places.) This P-value (and test statistic) leads to a decision to... reject the null accept the null fail to reject the null reject the alternative As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the assertion that there is a different proportion of only children in the G&T program. There is not sufficient evidence to warrant rejection of the assertion that there is a different proportion of only children in the G&T program. The sample data support the assertion that there is a different proportion of only children in the G&T program.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

12/9/23, 10:06 PM Chapter 9 Hypothesis Tests for a Single Population Proportion (counts towards your grade) https://egcc.instructure.com/courses/40375/assignments/1211620?module_item_id=3857931 10/16 Question 8 1/1 pt Details There is not sufficient sample evidence to support the assertion that there is a different proportion of only children in the G&T program. Question Help: Message instructor The US Department of Energy reported that 49% of homes were heated by natural gas. A random sample of 302 homes in Oregon found that 166 were heated by natural gas. Test the claim that proportion of homes in Oregon that were heated by natural gas is different than what was reported. Use a 10% significance level. Give answer to at least 4 decimal places. a. What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.) H 0 : .49 H 1 : .49 Based on the hypotheses, compute the following: b. Test Statistic = 2.0743 c. p-value = .0381 d. Based on the above we choose to e. The correct summary would be: that the proportion of homes in Oregon that were heated by natural gas is different than what the DOE reported value of 49%. Question Help: p = p ≠ Reject the null hypothesis There is enough evidence to support the claim Video Message instructor

12/9/23, 10:06 PM Chapter 9 Hypothesis Tests for a Single Population Proportion (counts towards your grade) https://egcc.instructure.com/courses/40375/assignments/1211620?module_item_id=3857931 11/16 Question 9 1/1 pt Details Question 10 1/1 pt Details left-tailed right-tailed two-tailed Test the claim that the proportion of men who own cats is smaller than 40% at the .05 significance level. The null and alternative hypothesis would be: The test is: In a random sample of 70 men, 38 men owned cats. The P-value of this sample is 0.9927 (to 4 decimals). Based on this we: We address the original claim with the conclusion. There is insufficient evidence that the proportion of men who own cats is smaller than 40% with .05 significance level. The proportion of men who own cats is smaller than 40% with .05 significance level. There is insufficient evidence to reject the proportion of men who own cats is 40% with .05 significance level. The proportion of men who own cats is not 40% with .05 significance level. The proportion of men who own cats is 40% with .05 significance level. Question Help: Fail to reject the null hypothesis Video Message instructor

12/9/23, 10:06 PM Chapter 9 Hypothesis Tests for a Single Population Proportion (counts towards your grade) https://egcc.instructure.com/courses/40375/assignments/1211620?module_item_id=3857931 12/16 A news article that you read stated that 59% of voters prefer the Democratic candidate. You think that the actual percent is smaller. 131 of the 225 voters that you surveyed said that they prefer the Democratic candidate. What can be concluded at the 0.01 level of significance? a. For this study, we should use b. The null and alternative hypotheses would be: Ho: .59 (please enter a decimal) H 1 : .59 (Please enter a decimal) c. The test statistic = -.237 (please show your answer to 3 decimal places.) d. The p-value = .4063 (Please show your answer to 4 decimal places.) e. The p-value is f. Based on this, we should the null hypothesis. g. Thus, the final conclusion is that ... The data suggest the population proportion is not significantly smaller 59% at = 0.01, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller 59%. z-test for a population proportion p = p < z > fail to reject

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

12/9/23, 10:06 PM Chapter 9 Hypothesis Tests for a Single Population Proportion (counts towards your grade) https://egcc.instructure.com/courses/40375/assignments/1211620?module_item_id=3857931 13/16 The data suggest the populaton proportion is significantly smaller 59% at = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller 59% The data suggest the population proportion is not significantly smaller 59% at = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 59%. h. Interpret the p-value in the context of the study. If the population proportion of voters who prefer the Democratic candidate is 59% and if another 225 voters are surveyed then there would be a 40.62% chance fewer than 58% of the 225 voters surveyed prefer the Democratic candidate. There is a 59% chance of a Type I error. If the sample proportion of voters who prefer the Democratic candidate is 58% and if another 225 voters are surveyed then there would be a 40.62% chance of concluding that fewer than 59% of all voters surveyed prefer the Democratic candidate. There is a 40.62% chance that fewer than 59% of all voters prefer the Democratic candidate. i. Interpret the level of significance in the context of the study. If the proportion of voters who prefer the Democratic candidate is smaller 59% and if another 225 voters are surveyed then there would be a 1% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is equal to 59%. If the population proportion of voters who prefer the Democratic candidate is 59% and if another 225 voters are surveyed then there would be a 1% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is smaller 59% There is a 1% chance that the earth is flat and we never actually sent a man to the moon. There is a 1% chance that the proportion of voters who prefer the Democratic candidate is smaller 59%.

12/9/23, 10:06 PM Chapter 9 Hypothesis Tests for a Single Population Proportion (counts towards your grade) https://egcc.instructure.com/courses/40375/assignments/1211620?module_item_id=3857931 14/16 Question 11 1/1 pt Details Hint: Help Helpful Videos: Calculations [+] Setup [+] Interpretations [+] Question Help: Message instructor You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly different from 79% at a level of significance of = 0.01. According to your sample, 71 out of 86 potential voters prefer the Democratic candidate. a. For this study, we should use b. The null and alternative hypotheses would be: Ho: .79 (please enter a decimal) H 1 : .79 (Please enter a decimal) c. The test statistic = .810 (please show your answer to 3 decimal places.) d. The p-value = .4179 (Please show your answer to 4 decimal places.) z-test for a population proportion p = p ≠ z

12/9/23, 10:06 PM Chapter 9 Hypothesis Tests for a Single Population Proportion (counts towards your grade) https://egcc.instructure.com/courses/40375/assignments/1211620?module_item_id=3857931 15/16 e. The p-value is f. Based on this, we should the null hypothesis. g. Thus, the final conclusion is that ... The data suggest the population proportion is not significantly different from 79% at = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 79%. The data suggest the population proportion is not significantly different from 79% at = 0.01, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 79%. The data suggest the populaton proportion is significantly different from 79% at = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 79% h. Interpret the p-value in the context of the study. There is a 41.78% chance of a Type I error. There is a 41.78% chance that the percent of all voters who prefer the Democratic candidate differs from 79%. If the population proportion of voters who prefer the Democratic candidate is 79% and if another 86 voters are surveyed then there would be a 41.78% chance that either more than 83% of the 86 voters surveyed prefer the Democratic candidate or fewer than 75% of the 86 voters surveyed prefer the Democratic candidate. If the sample proportion of voters who prefer the Democratic candidate is 83% and if another 86 voters are surveyed then there would be a 41.78% chance that we would conclude either fewer than 79% of all voters prefer the Democratic candidate or more than 79% of all voters prefer the Democratic candidate. i. Interpret the level of significance in the context of the study. If the population proportion of voters who prefer the Democratic candidate is 79% and if another 86 voters are surveyed then there would be a 1% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is different from 79% > fail to reject

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

12/9/23, 10:06 PM Chapter 9 Hypothesis Tests for a Single Population Proportion (counts towards your grade) https://egcc.instructure.com/courses/40375/assignments/1211620?module_item_id=3857931 16/16 There is a 1% chance that the earth is flat and we never actually sent a man to the moon. There is a 1% chance that the proportion of voters who prefer the Democratic candidate is different from 79%. If the proportion of voters who prefer the Democratic candidate is different from 79% and if another 86 voters are surveyed then there would be a 1% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is equal to 79%.

Chapter 9 Hypothesis Tests for a Single Population Proportion (counts towards your grade)

Related Documents