Cameron University Null Hypothesis and Confidence Interval Statistics Questions

Question Description

I’m working on a statistics multi-part question and need an explanation and answer to help me learn.

1) Suppose that Crown Bottling Company decides to use a level of significance of ? = 0.01, and suppose a random sample of 37 bottle fills is obtained from a test run of the filler. For each of the following four sample means®bsp;x??x®bsp;= 16.06, x??x®bsp;= 15.96, x??x®bsp;= 16.03, and x??x®bsp;= 15.93 /p>

a) determine whether the fillerænbsp;initial setup should be readjusted. In each case, use a critical value, a p-value, and a confidence interval. Assume that ? equals .1. (Round your z to 2 decimal places and p-value to 4 decimal places and CI to 3 decimal places.)

x®bsp;= 16.06

b) xænbsp;= 15.96

c) xænbsp;= 16.03

d) xænbsp;= 15.93

2) An article in Fortune magazine reported on the rapid rise of fees and expenses charged by mutual funds. Assuming that stock fund expenses and municipal bond fund expenses are each approximately normally distributed, suppose a random sample of 12 stock funds gives a mean annual expense of 1.65 percent with a standard deviation of 0.22 percent, and an independent random sample of 12 municipal bond funds gives a mean annual expense of 0.84 percent with a standard deviation of 0.20 percent. Let /em>1 be the mean annual expense for stock funds, and let /em>2 be the mean annual expense for municipal bond funds. Do parts a, b, and c by using the equal variances procedure.

a) Set up the null and alternative hypotheses needed to attempt to establish that the mean annual expense for stock funds is larger than the mean annual expense for municipal bond funds. Test these hypotheses at the 0.05 level of significance. (Round your sp2 answer to 4 decimal places and t-value to 2 decimal places.)

b) Set up the null and alternative hypotheses needed to attempt to establish that the mean annual expense for stock funds exceeds the mean annual expense for municipal bond funds by more than 0.5 percent. Test these hypotheses at the 0.05 level of significance.

c) Calculate a 95 percent confidence interval for the difference between the mean annual expenses for stock funds and municipal bond funds. Can we be 95 percent confident that the mean annual expense for stock funds exceeds that for municipal bond funds by more than .5 percent?

3) In the book Business Research Methods, Donald R. Cooper and C. William Emory (1995) discuss a manager who wishes to compare the effectiveness of two methods for training new salespeople. The authors describe the situation as follows:

The company selects 22 sales trainees who are randomly divided into two equal experimental groupsîe receives type A and the other type B training. The salespeople are then assigned and managed without regard to the training they have received. At the yearænbsp;end, the manager reviews the performances of salespeople in these groups and finds the following results: (I will put the picture for this one)

a) Set up the null and alternative hypotheses needed to attempt to establish that type A training results in higher mean weekly sales than does type B training.

b) Because different sales trainees are assigned to the two experimental groups, it is reasonable to believe that the two samples are independent. Assuming that the normality assumption holds, and using the equal variances procedure, test the hypotheses you set up in part a at level of significance .10, .05, .01 and .001. How much evidence is there that type A training produces results that are superior to those of type B?

4) Suppose a sample of 49 paired differences that have been randomly selected from a normally distributed population of paired differences yields a sample mean of d??=5.9du.9 and a sample standard deviation of sd = 6.9.

a) Calculate a 95 percent confidence interval for = /em>1 ®bsp;/em>2.

b) Test the null hypothesis H0: = 0 versus the alternative hypothesis Ha: ? 0 by setting ? equal to .10, .05, .01, and .001. How much evidence is there that differs from 0

5) Assume that we have selected two independent random samples from populations having proportions p1 and p2 and that pp^1 = 800/1000 = .8 and p°^2 = 950/1000 = .95. Test H0: p1 ®bsp;p2 > ±2 versus Ha: p1 ®bsp;p2 < ±2 by using a p-value and by setting ? equal to .10, .05, .01, and .001. How much evidence is there that p2 exceeds p1 by more than .12?

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