2) A researcher claims that the monthly consumption of coffee per person is more than 19 cups. In a sample of 60 randomly selected people, the mean monthly consumption was 20. The standard deviation of the sample was 4 cups. Find the p-value of the test. On the basis of the p-value is the researchers claim valid at a =0.01? Solution: I. Statement of the Hypothesis: Но H1 П. Statistical Test: III. Level of Significance and Critical Value: IV. Computed value of Z:
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- A student at a four-year college claims that mean enrollment at four-year colleges is higher than at two-year colleges in the United States. Two surveys are conducted. Of the 35 four-year colleges surveyed, the mean enrollment was 5,466 with a standard deviation of 8,191. Of the 35 two-year colleges surveyed, the mean enrollment was 5,068 with a standard deviation of 4,777. Test the student's claim at the 0.10 significance level. a) The null and alternative hypothesis would be: OHO: HF = HT H₁: HF HT O H₁: HF = HT H₁: PF PT t O Ho: PF = PT H₁: PF PT b) Determine the test statistic. Round to two decimals. c) Find the p-value and round to 4 decimals. p= d) Make a decision. O Reject the null hypothesis O Fail to reject the null hypothesis e) Write the conclusion. O There is not sufficient evidence to support the claim that enrollement is high at a four-year college than a two-year college. O There is sufficient evidence to support the claim that enrollement is high at a four-year…A student at a four-year college claims that mean enrollment at four-year colleges is higher than at two-year colleges in the United States. Two surveys are conducted. Of the 35 four-year colleges surveyed, the mean enrollment was 5,466 with a standard deviation of 8,191. Of the 35 two-year colleges surveyed, the mean enrollment was 5,068 with a standard deviation of 4,777. Test the student's claim at the 0.10 significance level.a) The null and alternative hypothesis would be: �0:��=���1:��>�� �0:��=���1:��≠�� �0:��=���1:��>�� �0:��=���1:��<�� �0:��=���1:��≠�� �0:��=���1:��<�� b) Determine the test statistic. Round to two decimals.�=c) Find the p-value and round to 4 decimals.p =It is claimed that the average weight of a bag of the biscuit is 250 grams with a standard deviation of 20.5 grams. A random sample of 50 bags of biscuits showed an average weight of 240 grams and the computed value for the test is -3.45. what is the appropriate interpretation of the test?
- (b) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. • The value of the test statistic is given by √n The p-value is the area under the curve to the right of the value of the test statistic. O One-tailed o Two-tailed Step 2: Enter the test statistic. (Round to 3 decimal places.) Step 3: Shade the area represented by the p- value. Step 4: Enter the p- value. (Round to 3 decimal places.) 0.3 0.2 0.1 (c) Based on your answer to part (b), choose what can be concluded, at the 0.05 level of significance, about the claim made by the studio. o Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean player rating is higher than 90. Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean player rating is higher than 90.…The mean number of eggs per person eaten in the United States is 244. Do college students eat a different number of eggs than the average American? The 60 college students surveyed averaged 255 eggs per person and their standard deviation was 64.4. What can be concluded at the a = 0.10 level of significance? a. For this study, we should use t-test for a population mean b. The null and alternative hypotheses would be: Но: 244 H1: PV A 244 c. The test statistic 1.323 (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.) e. The p-value is ? Va f. Based on this, we should Select an answer v the null hypothesis. g. Thus, the final conclusion is that ... O The data suggest that the populaton mean is significantly different from 244 at a = 0.10, so there is statistically significant evidence to conclude that the population mean number of eggs consumed by college students per year is different from 244. O The data suggest that the…The mean number of eggs per person eaten in the United States is 255. Do college students eat less eggs than the average American? The 68 college students surveyed averaged 246 eggs per person and their standard deviation was 30.5. What can be concluded at the a = 0.05 level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Ho: ?v Select an answer v Select an answer Y c. The test statistic ? (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.) e. The p-value is ? v f. Based on this, we should Select an answer v the null hypothesis.
- Suppose that another sample of resting heart rates for five MAT 110 students was obtained: 72, 68, 66, 69, and 74 beats per minute. The standard deviation of this sample is approximately 3.19 BPM. Are the data values in this sample, or in your sample more spread out? Explain how you know. The resting heart rates for the other students were 66,67,69,70 and 71 with a deviation of 3.438The mean number of eggs per person eaten in the United States is 266. Do college students eat a different number of eggs than the average American? The 61 college students surveyed averaged 285 eggs per person and their standard deviation was 72.6. What can be concluded at the a= 0.10 level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Но: v Select an answer H.: vSelect an answer c. The test statistic ? (please show your answer to 3 decimal places.) d. The p-value = e. The p-value is ? f. Based on this, we should Select an answer v the null hypothesis. g. Thus, the final conclusion is that ... (Please show your answer to 4 decimal places.) a O The data suggest that the sample mean is not significantly different from 266 at a = 0.10, so there is statistically insignificant evidence to conclude that the sample mean number of eggs consumed by college students per year is different from 285. O The data suggest that the…A tire company claims that the lifetimes of its tires average 50,000 miles. The standard deviation of tire lifetimes is known to be 5,261 miles. You sample 100 tires and will test the hypothesis that the mean tire lifetime is at least 50,000 miles against the alternative that it is less. Assume, in fact, that the true mean lifetime is 49,545 miles. It is decided to reject Ho if the sample mean is less than 48,894. Find the level and power of this test. 0 Round your answers to four decimal places. Level of the test = Power of the test =
- The mean SAT score in mathematics is 228. The standard deviation of these scores is 30. A special preparation course claims that the mean SAT score, H, of its graduates is greater than 258. An independent researcher tests this by taking a random sample of 20 students who completed the course; the mean SAT Score in mathematics for the sample was 209. At the 0.05 level of significance, can we conclude that the population mean SAT score for graduates of the course is greater than 2587 Assume that the population standard deviation of the scores of course graduates is also 30. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) state the null hypothesis H, and the alternative hypothesis H. H :0 H :0 (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more…Over the years, the mean customer satisfaction rating at a local restaurant has been s0. The restaurant was recently remodeled, and now the management claims the mean customer rating, u, is not equal to so. In a sample of 54 customers chosen at random, the mean customer rating is 75.4. Assume that the population standard deviation of customer ratings is 21.2. Is there enough evidence to support the claim that the mean customer rating is different from so? Perform a hypothesis test, using the 0.0s level of significance. (a) State the null hypothesis , and the alternative hypothesis OSO H: D (b) Perform a z-test and find the p-value. Here is some information to help you with your z-test. • The value of the test statistic is given by • The p-value is two times the area under the curve to the left of the value of the test statistic. Normal Distribution Step 1: Select one-tailed or two-tailed O One-tailed O Two-tailed Step 2: Enter the test statistic. (Round to 3 decimal places.) (Round to…The mean SAT score in mathematics, u, is 596. The standard deviation of these scores is 47. A special preparation course clalms that its graduates will score higher, on average, than the mean score 596. A random sample of 90 students completed the course, and their mean SAT score in mathematics was 608. At the 0.05 level of significance, can we condude that the preparation course does what it claims? Assume that the standard deviation of the scores of course graduates is also 47. Perform a one-talled test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. H, :0 H, :0 (b) Determine the type of test statistic to use. OSO (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the critical value. (Round to three or more decimal…