Question

Be sure to 1) give the null and alternative hypotheses, 2) label which hypothesis is the claim, 3) Identify whether the test is left-tailed, right-tailed, or two-tailed, 4) name the test being used, 5) find the P-value for the sample, 6) state whether you reject or fail to reject the null hypothesis, and 7) give the conclusion in the context of the problem.

3. A student at South Plains College claims that the average cost of textbook is more than $75 dollars. Test this student’s claim using a 0.05 level of significance. A random sample of 15 textbooks had an average price of $78.15 and a standard deviation of $8.80. (9 pts)

4. The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. A sample of 54 bears has a mean weight of 182.9 lbs and it has previously been found that the population standard deviation of bear weights is 81.8 lb. Use a 0.10 level of significance to test the claim that the population mean of all such bear weights is less than 200 lb. (9 pts)

5. It has been believed that one in four Americans (25%) relies on unconventional medicine. Test this claim using a 0.01 level of significance if a recent study reported in the New England Journal of Medicine found that in a random sample of 1,539 adults, 428 of them used some form of unconventional medicine. (9 pts)

6.   A medical researcher wishes to see whether the pulse rates of smokers are higher than the pulse rate of nonsmokers. Samples of 100 smokers and 100 nonsmokers are selected. The results are shown below. Using a level of significance of 0.05, test the claim that smokers have higher pulse rates than nonsmokers. (9 pts) Also, find the 90% confidence interval for the differences of the means. (3 pts)

       Smokers                                        Nonsmoker

x1 = 90 x2 = 88

s1 = 5 s2 = 6

n1 = 100 n2 = 100

Answer 1

Question 3:

We have to test the hypothesis that

The average cost of text book is more than $75 dollars.

i.e. Null Hypothesis:

against

Alternative Hypothesis- ( Right-tailed test)

Given:

n = 15, xbar = 78.15 and s= 8.80

Since sample size is small and population standard deviation is unknown, we use one sample t-test for testing mean.

The value of test statistic is

Under Ho the value of test statistic is

t = 1.3864

Alpha : level of significance = 0.05

Since test is right-tailed and value of test statistic is 1.3864, p-value is obtained by

Decision : Since p-value > level of significance alpha. We failed to reject Ho.

Conclusion : There is not sufficient evidence support to claim that average cost of text book is more than $ 75 dollars.

Question 4 :

We have to test the hypothesis that

The mean weight of bear is less than 200 lb.

i.e. Null Hypothesis:

against

Alternative Hypothesis- ( left-tailed test)

Given:

n = 54, xbar = 182.9 and s= 81.8

Since population standard deviation is unknown, we use one sample t-test for testing population mean..

The value of test statistic is

Under Ho the value of test statistic is

Alpha : level of significance = 0.10

Since test is right-tailed and value of test statistic is -1.5362, p-value is obtained by

Decision : Since p-value < level of significance alpha. We reject Ho.

Conclusion : There is sufficient evidence support to claim that mean weight of bear is less than 200 lb.

Question 5 :

Let P : Population proportion of Americans relies on unconventional medicine.

We have to test the hypothesis

Proportion of Americans relies on unconventional medicine is 25% .

i.e. Null Hypothesis-

against

Alternative Hypothesis- (two -tailed test)

n = number of adults in a sample = 1539

X : Number of adults relies on unconventional medicine = 428

p : Sample proportion of Americans relies on unconventional medicine = X/n = 428 / 1539 = 0.2781

We used one sample z-test for testing population proportion.

The value of test statistic is

Under Ho, the value of test statistic is

Alpha: level of significance = 0.01

Since the test is two-tailed and value of test statistic is 2.5458, p-value is obtained by

Decision : Since p-value > level of significance alpha. We failed to reject Ho.

Conclusion : There is sufficient evidence support to claim that Proportion of Americans relies on unconventional medicine is 25%.

Question 6 :

Consider

X₁ : Pulse rate of smokers

X₂ : Pulse rate of non- smokers

Given:

n₁ = 100 , n₂ = 100

Xbar1 = 90 , xbar2 = 88

s1 = 5, s2 = 6

Let   : Mean pulse rate of smokers.

: Mean pulse rate of non-smokers.

We have to test the hypothesis that

The pulse rate of smokers is higher than pulse rate of non-smokers.

i.e. Null Hypothesis -

against

Alternative Hypothesis- (Right-tailed test).

Since sample size is large, we used Z-test for testing difference in means.

The value of test statistic is

Under Ho, the value of test statistic

Alpha: level of significance = 0.05

Since the test is two-tailed and value of test statistic is 2.5607, p-value is obtained by

Decision : Since p-value < level of significance alpha. We reject Ho.

Conclusion : There is sufficient evidence support to claim that the pulse rate of smokers is higher than pulse rate of non-smokers.

90% confidence interval for the difference in means is

= ( 2 - 1.645 * 0.7810 , 2 + 1.645 * 0.7810)

= ( 0.7153, 3.2847)