Test the claim that the mean GPA of night students is significantly different than 2.7 at the 0.01 significance level.
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Test the claim that the
The null and alternative hypothesis would be:
H1:p≠0.675
H1:μ<2.7
H1:μ>2.7
H1:p<0.675
H1:μ≠2.7
The test is:
Based on a sample of 45 people, the sample mean GPA was 2.73 with a standard deviation of 0.02
The test statistic is: (to 4 decimals)
The p-value is: (to 4 decimals)
Based on this we:
- Fail to reject the null hypothesis
- Reject the null hypothesis
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- As part of a water quality survey, you test the water hardness in several randomly selected streams. The results are shown below. Construct a confidence interval for the population variance sigma squaredσ2 and the population standard deviation sigmaσ. Use a 90% level of confidence. Assume that the population has a normal distribution. n =25 s =19 grains per gallonYou work for a soft-drink company in the quality control division. You are interested in the standard deviation of one of your production lines as a measure of consistency. The product is intended to have a mean of 12 ounces, and your team would like the standard deviation to be as low as possible. You gather a random sample of 14 containers. Estimate the population standard deviation at a 80% level of confidence. 12.07 12.15 12.01 11.92 12.04 12.11 12.03 11.9 12.01 11.99 11.88 12.04 11.97 12.02 (Data checksum: 168.14) Note: Keep as many decimals as possible while making these calculations. If possible, keep all answers exact by storing answers as variables on your calculator or computer. a) Find the sample standard deviation: b) Find the lower and upper x critical values at 80% confidence: Lower: Upper: c). Report your confidence interval for o: (What is the test statistic and P value?
- You work for a soft-drink company in the quality control division. You are interested in the standard deviation of one of your production lines as a measure of consistency. The product is intended to have a mean of 12 ounces, and your team would like the standard deviation to be as low as possible. You gather a random sample of 14 containers. Estimate the population standard deviation at a 90% level of confidence. 12.07 11.96 11.93 12.16 12.06 11.9 12.06 12.21 11.86 12.03 11.86 11.83 11.99 12.09 (Data checksum: 168.01) Note: Keep as many decimals as possible while making these calculations. If possible, keep all answers exact by storing answers as variables on your calculator or computer. a) Find the sample standard deviation: b) Find the lower and upper χ2χ2 critical values at 90% confidence:Lower: Upper: c) Report your confidence interval for σσ: ( , )You wish to test the following claim (Ha) at a significance level of a = 0.005. H.: µ = 60.8 H.:u > 60.8 You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: data 92.4 61.2 97.2 82.3 What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) a O greater than a This test statistic leads to a decision to... o reject the null o accept the null o fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 60.8. There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 60.8. The sample data support the claim that the population mean is greater than 60.8. There is…Choose the appropriate statistical test. When computing, be sure to round each answer as indicated. A dentist wonders if depression affects ratings of tooth pain. In the general population, using a scale of 1-10 with higher values indicating more pain, the average pain rating for patients with toothaches is 6.8. A sample of 30 patients that show high levels of depression have an average pain rating of 7.1 (variance 0.8). What should the dentist determine? 1. Calculate the estimated standard error. (round to 3 decimals). [st.error] 2. What is thet-obtained? (round to 3 decimals). 3. What is the t-cv? (exact value) 4. What is your conclusion? Only type "Reject" or Retain"
- You work for a soft-drink company in the quality control division. You are interested in the standard deviation of one of your production lines as a measure of consistency. The product is intended to have a mean of 12 ounces, and your team would like the standard deviation to be as low as possible. You gather a random sample of 14 containers. Estimate the population standard deviation at a 90% level of confidence. 11.9 12.02 11.91 11.93 12.01 12.08 12.07 11.85 12.02 12.15 12.02 11.88 12.05 11.81 (Data checksum: 167.7) Note: Keep as many decimals as possible while making these calculations. If possible, keep all answers exact by storing answers as variables on your calculator or computer. a) Find the sample standard deviation: b) Find the lower and upper χ2χ2 critical values at 90% confidence:Lower: Upper: c) Report your confidence interval for σσ: ( , )Q: Fewer than 90% of adults have a cell phone. This is a claim about a population proportion so a normal distribution is assumed. The claim undergoes a hypothesis test using a significance level of α = 0.05. The P-value based on sample data is calculated to be 0.0003. On your graph, next highlight the P-value. (The P-value means that there is a 0.03% chance that your results could be random or happen by chance). State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.) Without using technical terms or symbols, state a final conclusion that addresses the original claim, i.e., fewer than 90% of adults have a cell phone.Now we will test this hypothesis using the critical value method. The z statistic is most relevant to this test. Using the z-score tables at the back of the textbook, find the z-score for a significance level of α = 0.05. This is the critical value. What is it? Sketch a normal distribution curve, plot the critical value, and highlight the critical…Fewer than 90% of adults have a cell phone. This is a claim about a population proportion so a normal distribution is assumed. The claim undergoes a hypothesis test using a significance level of α = 0.05. The P-value based on sample data is calculated to be 0.0003. 1. State the null hypothesis and alternative hypothesis. 2. What kind of test would this be - two-tailed, left-tailed or right-tailed? 3. Sketch a normal distribution curve and highlight the region of significance. On your graph, next highlight the P-value. 4. State a conclusion about the null hypothesis (reject H0 or fail to reject H0).
- You work for a soft-drink company in the quality control division. You are interested in the standard deviation of one of your production lines as a measure of consistency. The product is intended to have a mean of 12 ounces, and your team would like the standard deviation to be as low as possible. You gather a random sample of 16 containers. Estimate the population standard deviation at a 90% level of confidence. 12.07 12.18 12.05 12.1 11.98 12.07 12.14 11.98 11.95 12.02 11.94 12.02 11.95 11.97 11.95 11.93 (Data checksum: 192.3) Note: Keep as many decimals as possible while making these calculations. If possible, keep all answers exact by storing answers as variables on your calculator or computer. a) Find the sample standard deviation: b) Find the lower and upper χ2χ2 critical values at 90% confidence:Lower: Upper: c) Report your confidence interval for σσ: ( , )In a test of hypothesis, the null hypothesis is that the population mean is equal to 90 and the alternative hypothesis is that the population mean is not equal to 90. A sample of 16 elements selected from this population produced a mean of 86.75 and a standard deviation of 12.54. The significance level is 2%. a. –2.602 and 2.602 b. –2.583 and 2.583 c. –2.131 and 2.131 d. –1.341 and 1.341The table below shows two samples taken to compare the mean age of individuals who purchased the iPhone at two AT&T store locations. Ann Arbor 25.817 Livonia 31.248 1.874 10 3.389 7 At a=05, can you conclude that the first sample has a larger variance than the second sample? Statistic Mean Standard Deviation. Sample size Multiple Choice No, the p-value>.05. Unclear because the p-value is approximately equal to 05. Yes, the p-value <.05. No because the p-value is approximately equal to 05