4. Determine the t-value in each of the cases (Round to three decimal places as needed.)

• Givenn= 85, find the t-value such that the area in the right tail is 0.025
• Find the t-value in the left tail such that= 0.005with 16 degrees of freedom
• Givenn=12,find the critical t-value in the left tail that corresponds to 99% confidence
• Find the critical t-value that corresponds to 98% confidence. Assume 34 degrees of freedom

5. In a random sample of 10 patients in a nursing home, it was determined that the mean age of patients that showed patterns of elevated blood pressure (BP) was 80 with a standard deviation of 5. Construct and interpret a 90% confidence interval for the mean age of patients showing patterns of elevated BP. The data comes from a population that is approximately normal with no outliers. Complete parts (a) through (c) below and show your work when necessary

• State the point estimate and verify the requirements for constructing a confidence interval
• Construct and interpret a 90% confidence interval for the mean age of patients showing patterns of elevated blood pressure(Round to three decimal places as needed.)

6. A container of detergent is labeled as containing 3 fluid liters. The quality control manager wants to verify that the processing plant equipment is neither over-filling nor under-filling the containers. Complete parts (a) through (d) below and show your work when necessary.

• State the null and alternative hypotheses that would be used to determine if the processing plant equipment is calibrated correctly (Type integers or decimals. Do not round.)
• The quality control manager obtains a sample of containers and measures the contents. The sample evidence leads the manager to reject the null hypothesis. Come up with a conclusion for this hypothesis test. (Hint: Do we have sufficient or not sufficient evidence?)
• Suppose, in fact, the processing plant equipment is not out of calibration. Has a Type I or Type II error been made? Explain your reason
• Management has informed the quality control department that it does not want to shut down the filling machine unless the evidence is overwhelming that the machine is out of calibration. What level of significance would you recommend the quality control manager to use? Explain.

7.A poll showed the approval rating to be 75%. A second poll based on 1000 randomly selected employees showed that775approved of the job the CEO was doing. Do the results of the second poll indicate that the proportion of employees who approve of the job the CEO is doing is significantly higher than the original level? Assume the= 0.05level of significance. Complete parts (a) through (d) and show your work

when appropriate.

• State the null and alternative hypothesis for this test using the appropriate symbols
• Find the tests statistic for this hypothesis test and state the appropriate symbol (Round to two decimal places as needed.)
• Determine the P-value for this hypothesis test (Round to three decimal places as needed.)
• State your conclusion

8. A biologist obtains a random sample of 20 zebra mice. The mice were placed in a maze and their intelligence was tested. It is known that IQs are normally distributed with a mean of 40. If the IQs of the 20 zebra mice in the study result in a sample mean of 45.3 and sample standard deviation of 10, is there evidence that the mice have lower IQs? Use the level of significance. Complete parts (a) through (d).Show your work when appropriate.

• State the null and alternative hypothesis for this test using the appropriate symbols
• Find the tests statistic for this hypothesis test and state the appropriate symbol (Round to two decimal places as needed.)
• Approximate the P-value range
• State your conclusion