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# Testing of hypothesis problems

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Question 1
For the given data, find (a) the point estimate of the population mean and (b) the margin of error for a 90% confidence interval. Lengths of work commute of 32 people (in miles):
12 9 7 2 8 7 3 27
21 10 13 3 7 2 30 7
6 13 6 14 4 1 10 3
13 6 2 9 2 12 16 18

Question 2
a. Find the critical value of tc for the confidence level c and the sample size n, noted below , using a two-sided test. C = 0.80 ; n = 22

b. Given c = 0.95 ; s = 0.05 ; n = 25 ; x(bar) = 3.5 (i) Find the margin of error. (ii)
Construct the confidence interval for &#956; using the statistics you have calculated above.

Question 3
Use a P- value to test the claim about the population mean &#956; using the given sample statistics. State your decision for &#945; = 0.05 Claim: &#956; &#8800; 230; Other values: x (bar) = 221.5 ; n = 36 ; and s - 17.3

Question 4
Use a t-test to investigate the claim and assume that the population is normally distributed:
A large university says the mean number of classroom hours per week for full-time faculty is more than 9. A random sample of the number of classroom hours for fulltime faculty for one week is listed. At &#945; = 0.05 , test the university's claim.
10.7 9.8 11.6 9.7 7.6 11.3 14.1 8.1 11.5 8.5 6.9

Question 5
Use the given sample statistics to test the claim about the difference between two population means &#956;1 and &#956;2 at the given level of significance &#945;. Assume the samples are random and independent and that the populations are approximately normally distributed, and that the population variances are unequal.
Claim: &#956;1 &#8805; &#956;2, &#945; = 0.1. Sample statistics:
x1 (bar) = 520, s1 = 25, n1 = 7
x2 (bar) = 500, s2= 55, n2 = 6

Question 6
Using a test for paired data, test the claim about the mean of the difference of the two populations at the given level of significance &#945; = 0.01 using the given statistics. Assume the populations are normally distributed, and that the population variances are unequal.
Claim: &#956;d < 0, &#945; = 0.01. Sample statistics:
d(bar) = 3.2, sd = 1.38, n1 = 25

Question 7
It is asserted that a greater proportion of males (= x 1 ) contribute to charity than females (= x 2 ). A survey of male and female contributors to charity showed that of 900 males surveyed, 86 contributed to charity, and of 1200 females surveyed, 107 contributed to charity. Assume the sample statistics are from random, independent samples.

State the Null, and Alternative , hypotheses to be tested, noting whether the test is a right-tailed, left-tailed , or two tailed test and test the hypothesis that the proportion of charitable givers are the same for both males and females. Test at the level &#945; = 0.05.

Question 8
Use the given contingency table to
(a) Find the expected frequencies of each cell in the table,
(b) Perform a chi-square test for independence, and
(c) Comment on the relationship between the two variables. Assume the variables are independent. The contingency table shows the results of a random sample of 500 individuals classified by gender and type of vehicle owned. Use &#945; = 0.01.

Question 9
The number of convertibles sold at a car dealership in a month and the average monthly temperature (in degree Fahrenheit) are given in the Table below :
a. Find the sample correlation coefficient r?
b. Determine whether there is a positive linear correlation, a negative linear correlation, or no correlation between the variables, and explain the results,
Convertible sold,
x 0 2 6 5 7 9
Average monthly temperature, y 40 48 58 62 72 79 noting particularly which variable is the dependent, and which the independent, one.
c. Is there enough evidence to conclude that there is a linear correlation between the number of convertibles sold and the average monthly temperature?
Use &#945; = 0.05 and show your work.

Question 10
A financial services institution claims that the median credit card debt among families with annual earnings of \$10,000 to \$24,999 is more than \$1200. The credit card debts (in thousands of dollars) among 13 randomly selected families are listed below. At &#945; = 0.01, can you support the institution's claim?
1.97 1.10 1.02 1.05 0.98 1.36 1.74 1.69 1.48 0.99 1.29 0.92 1.45
Use a sign test to test the claim by doing the following:
a. Write the claim mathematically and identify Ho and Ha.
b. Determine the critical value.
c. Calculate test statistics.
d. Decide whether to reject or fail to reject the null hypothesis.
e. Interpret the decision in the context of the original claim.