5 Liter Beer

1. Suppose we take a random sample of 100 from a normally distributed population with an average population 25 years and a population standard deviation of 4. What can we say about the sampling distribution of the sample mean?

(A) The sampling distribution is normal with an average of 25 and a standard deviation of 4.
(B) the sampling distribution is normal with an average of 25 and a standard deviation of 0.4.
(C) The sampling distribution is normal with an average of 2.5 and a standard deviation of 4.
(D) The sampling distribution is normal with an average of 2.5 and a standard deviation of 0.4.
(E) None of the above statements are true.

Answer: ____________________________

2. Suppose we have a population normally distributed with a mean of 100 and a standard deviation of 15. If we take a random sample of 30 from this population, what is the probability that the sample average is above 96?











Answer: __________________________







3. A researcher says the average cost of a hot dog in his city is $ 1.50. A random sample of 100 hot dogs had an average price of $ 1.35 and a standard deviation of $ 0.05. If I had to test the researcher's request to  = 0.01, which is the numerical value of the test statistic?







Answer: _______________________________

4. Homer wants to test if its beer increases IQ, then it randomly chooses 6 people to test the beer. It gives everyone an IQ test, one liter of beer, then another IQ test. The results are given in the following table:

Before 100 110 98 150 88 120
After 90 100 103 145 90 123

Construct a confidence interval 90% of the average increase in IQ. (Note: It is important which way you avoid this problem.)










Answer: (_______________, ______________)

5. If we wanted to make a hypothesis test on data in the previous problem, this test should be used?

(A) 2-sample t-test for independent samples
(B) one way ANOVA
(C) 1-sample z-test
(D) paired t-test
(E) None of these answers


Answer: ___________

6. Suppose we open a large bag of 200 M-and-M and found 45 pieces red. Does the sample data provide enough evidence at the 0.05 significance for us to conclude that over 15% of m-and-M are red? (The hypothesis test appropriate conduct and complete the form below.)

H0: ________________________________________ ...

Ha: ________________________________________ ...

 �e� = 0.05






Test Statistic: _______________________________________





P-value or critical value (s): ________________________

Conclusion



















7. Suppose we take a random sample of 30 adult men. Suppose that the sample had a mean systolic pressure of 130 with a standard deviation of 25. Construct a confidence interval 99% for the average systolic blood pressure.










Answer: (_____________, _________________)

8. If we are conducting a bilateral z-test and the test statistic has a value of -2.37 and the significance level is 0.10, determine the value of p.










Answer: _______________________

9. If we make a hypothesis test the null hypothesis that "Bob does not weigh more than Joe did, which of the following would be a Type II error?

(A final) that weighs more than Joe Bob.