For Multiple Choice Questions, please explain and show your work. All other questions please SHOW YOUR WORK.
_____1. Which of the following will decrease the probability of a Type I error?
a. Decrease power
b. Increase power
c. Increase significance level
d. 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 daily temperature of Boston was the same as the mean daily temperature of New York. His alternative hypothesis was that mean temperatures in these two cities were different. He computed a p-value of 0.094. Using a confidence level of 90%, he should conclude:
a. In September, Boston was colder than New York
b. In September, New York was colder than Boston
c. Reject the null hypothesis
d. Fail to reject the null hypothesis
e. None of the above.
_____3. The value of “t” will increase as the standard deviation of the difference _____ and the difference between means ____.
a. increase; decreases
b. increases; increases
c. decreases; decreases
d. decreases; increases
e. 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 0
b. If a 99% confidence interval contains 0, then the 95% confidence interval contains 0
c. If a 95% confidence interval contains 1, then the 99% confidence interval contains 1
d. If a 99% confidence interval contains 1, then the 95% confidence interval contains 1
e. None of the above are correct about confidence intervals.
_____5. Imagine a researcher presented a null hypothesis that in a certain community, the average energy expenditure of residents is at least 2,100 calories per day. He randomly sampled 100 residents in that 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 day
b. The average energy expenditure is less than 2,100 calories per day
c. The average energy expenditure is not equal to 2,100 calories per day
d. Fail to reject the null hypothesis
e. 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 participants’ blood pressure before and after the drug was administered. If we want to compare the mean blood pressure from the two time-periods with a two-tailed t test, how many degrees of freedom are there?
a. 34
b. 35
c. 68
d. 69
e. 70 STAT 200 (7962)
_____7. In a statistical hypothesis test, how is the rejection region impacted when α, the level of significance, is increased?
a. The answer depends on the value of β
b. The size of the rejection region decreases
c. The size of the rejection region increases
d. The rejection region is unaltered
e. None of the above.
8. _____ The UMUC bookstore states the average textbook costs $119. A randomly selected sample of 26 new textbooks at the UMUC bookstore had a mean price of $123.45 and sample standard deviation of $15.23. Use a 0.05 significance level to test the claim that the mean price of textbooks at the UMUC bookstore 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