For Multiple Choice Questions, please explain and show your work. All other questions please SHOWYOUR WORK._____1. Which of the following will decrease the probability of a Type I error?a. Decrease powerb. Increase powerc. Increase significance leveld. Decrease significant level e. Use normal distribution vice t-distribution_____2. A weatherman stated a null hypothesis that during the month of September, the mean dailytemperature of Boston was the same as the mean daily temperature of New York. His alternativehypothesis was that mean temperatures in these two cities were different. He computed a p-value of0.094. Using a confidence level of 90%, he should conclude:a. In September, Boston was colder than New Yorkb. In September, New York was colder than Bostonc. Reject the null hypothesisd. Fail to reject the null hypothesise. None of the above._____3. The value of âtâ will increase as the standard deviation of the difference _____ and thedifference between means ____.a. increase; decreasesb. increases; increasesc. decreases; decreasesd. decreases; increasese. None of the above._____4. Which of the following descriptions of confidence intervals is correct? (Select all that apply)a. If a 95% confidence interval contains 0, then the 99% confidence interval contains 0b. If a 99% confidence interval contains 0, then the 95% confidence interval contains 0c. If a 95% confidence interval contains 1, then the 99% confidence interval contains 1d. If a 99% confidence interval contains 1, then the 95% confidence interval contains 1e. None of the above are correct about confidence intervals._____5. Imagine a researcher presented a null hypothesis that in a certain community, the averageenergy expenditure of residents is at least 2,100 calories per day. He randomly sampled 100 residents inthat particular community. He computed a negative test statistic and the associated p-value was 0.08.Given a 90% confidence level, he should conclude:a. The average energy expenditure is greater than 2,100 calories per dayb. The average energy expenditure is less than 2,100 calories per dayc. The average energy expenditure is not equal to 2,100 calories per dayd. Fail to reject the null hypothesise. None of the above_____6. A researcher wanted to test the effect of a new drug on reducing blood pressure. In the study,there were 35 participants. The researcher measured the participantsâ blood pressure before and afterthe drug was administered. If we want to compare the mean blood pressure from the two time-periodswith a two-tailed t test, how many degrees of freedom are there?a. 34b. 35c. 68d. 69e. 70 STAT 200 (7962)_____7. In a statistical hypothesis test, how is the rejection region impacted when α, the level ofsignificance, is increased?a. The answer depends on the value of βb. The size of the rejection region decreasesc. The size of the rejection region increasesd. The rejection region is unalterede. None of the above.8. _____ The UMUC bookstore states the average textbook costs $119. A randomly selected sample of26 new textbooks at the UMUC bookstore had a mean price of $123.45 and sample standard deviationof $15.23. Use a 0.05 significance level to test the claim that the mean price of textbooks at the UMUCbookstore is significantly more than $119 (use the p-value method). SHOW YOUR WORK.a. Give the symbolic null & alternative hypotheses. Use proper notation.H0:HA:b. Determine the test statistic (round to 3 decimal places):c. Determine the p-value (round to 3 decimal places):d. Result (Circle one & justify):REJECT ��FAIL TO REJECT ��Reason:e. State a conclusion within the context of the scenario:9. In a study of proctored and non-proctored tests in an online course, researchesobtained the data below:Group 1 (Proctored): � = 30, �̅= 74.30, � = 12.87Group 2 (Non-proctored): � = 32, �̅= 80.62, � = 22.09Use of 0.05 significance level to test the claim that students taking non-proctored tests get ahigher mean than those taking proctored tests (use the p-value method). SHOW YOUR WORK.HINT: See Illowsky, Chapter 10.a. Give the symbolic null & alternative hypotheses. Use correct notation.H0:HA:b. Determine the test statistic (round to 3 decimal places): __________________c. Determine the p-value (round to 3 decimal places):d. Result (Circle one & justify):REJECT ��FAIL TO REJECT ��Reason:e. State a conclusion within the context of the scenario:10. Listed below are body temperatures for four subjects measured at two different timesin a day.Body Temperature (°�) ��6 �� : 98.0, 97.0, 98.6, 97.4Body Temperature (°�) �� 6 �� : 98.0, 97.6, 98.8, 98.0Assume the sample data are simple random samples and that the differences have a distributionthat is approximately normal. Test the claim that body temperature measured at 6 pm is higherthan the body temperature measured at 6 am. Use a 0.10 significance level. SHOW YOUR WORKa. Give the symbolic null & alternative hypotheses. Use correct notation.H0:HA:b. Determine the test statistic (round to 3 decimal places): __________________c. Determine the p-value (round to 3 decimal places):d. Result (Circle one & justify):REJECT ��Reason:e. State a conclusion within the context of the scenario:FAIL TO REJECT ��
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