Problem 1.

Population 1 is known to have 1=2.34. A sample of size 49 from population 1 had a mean of 30.1436. Population 2 is known to have 2=2.17. A sample of size 47 from population 2 had a mean of 29.1722. To conduct the hypothesis test the claim that 1 and 2 are different, determine each of the following:

A. The value of the test statistic: ______________________

B. The p-value is approximately ____________________

Problem 2.

(5 points) The hypothesis test

H0:d0

H1:d<0 is to be carried out for a random sample of 37. d=1.2 and the test statistic is found to be t=0.503401036990197. What is the standard deviation for the differences in the sample?

sd=__________

Problem 3.

Suppose that we are to conduct the following hypothesis test:

H0: 51

H1: < 51

Suppose is known, and sampling lead to a test statistic of zc=2.21

The p-value is

For =0.005, what would be the decision for the hypothesis test? A. There is not enough evidence to support the claim that <51 B. There is not enough evidence to support the claim that 51 C. There is enough evidence to support the claim that <51 D. There is enough evidence to support the claim that 51

Problem 4.

Two statistics teachers both believe that each has the smarter class. To put this to the test, they give the same final exam to their students. A summary of the class sizes, class means, and standard deviations is given below:

n1=13 x1=82.2 s1=18

n2=24, x2=77.1, s2=18.7

Is there evidence, at an =0.1 level of significance, to conclude that there is a difference in the two classes? Carry out an appropriate hypothesis test, filling in the information requested.

A. The value of the test statistic: ____________

B. The degree of freedom for the distribution: __________

For the next part, it is strongly recommended that you use the tables provided by the class

C. The approximate range of values for the p-value: ______________< p-value < _____________

D. Your decision for the hypothesis test: A. Do Not Reject H0. B. Reject H0. C. Reject H1. D. Do Not Reject H1.

Problem 5.

The hypothesis test

H0:120

H1:12<0 is to be carried out for two populations. One population, called population 1, is known to have a standard deviation of 9.7. The second population, called population 2, is known to have a standard deviation of 6.4. A random sample of 24 from population 1 has a mean of 48.5 and a standard deviation of 11.2. A random sample of 30 from population 2 has a standard deviation of 10.4. The test statistic for the hypothesis test had a value of -2.00080. What was the mean of the sample from population 2?

x2 =

Problem 6.

(5 points) Golf-course designers have become concerned that old courses are becoming obsolete since new technology has given golfers the ability to hit the ball so far. Designers, therefore, have proposed that new golf courses need to be built expecting that the average golfer can hit the ball more than 250 yards on average. Based off of collected information, the standard deviation of all driving distences is 43.2 yards. A random sample of 194 golfers had a mean driving distance of 256.7925 yards.

Conduct a hypothesis test where H0:250 and H1:>250 by computing the following: (a) test statistic ________ (b) p-value p= _______ (c) If this was a two-tailed test, then the p-value is __________

Problem 7.

Two independent samples have been selected, 65 observations from population 1 and 50 observations from population 2. The sample means have been calculated to be x1=13.1 and x2=8.6. From previous experience with these populations, it is known that the variances are 2/1=33 and 2/2=37.

For the hypothesis test of H0:(12)0 and Ha:(12)>0 Use =0.02=0.02. (a) Compute the test statistic. z=____________

(b) Find the approximate p-value pvalue=____________

The final conclustion is

A. We can reject the null hypothesis that (12)0 and accept that (12)>0. B. There is not sufficient evidence to reject the null hypothesis that (12)0.

Question 8) A random sample of 150 observations is selected from a binomial population with unknown probability of success pp. The computed value of p^ is 0.73. For the following hypothesis tests, compute the test statistic. (1) Test H0:p0.65 against H1:p>0.65.

test statistic z=________

(2) Test H0:p0.55 against H1:p<0.55.

test statistic z=________

(3) Test H0:p=0.5against H1:p0.5.

test statistic z=________

Problem 9.

Suppose that we fail to reject a null hypothesis at the 0.01 level of significance. Then for which of the following values do we also fail to reject the null hypothesis? A. 0.015 B. 0.1 C. 0.005 D. 0.2 E. 0.02

Problem 10.

A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 70 women over the age of 50 used the new cream for 6 months. Of those 70 women, 62 of them reported skin improvement (as judged by a dermatologist). Is this evidence that the cream will improve the skin of more than 40% of women over the age of 50? Test using =0.01.

test statistic z=_________

The final conclusion is

A. There is not sufficient evidence to reject the null hypothesis that p=0.4. That is, there is not sufficient evidence to reject that the cream can improve the skin of more than 40% of women over 50. B. We can reject the null hypothesis that p=0.4 and accept that p>0.4. That is, the cream can improve the skin of more than 40% of women over 50.