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Chapter 7: Q118S (page 442)

Effectiveness of online courses. The Survey of Online Learning, 鈥淕rade Level: Tracking Online Education in the United States, 2014,鈥� reported that 74% of college leaders believe that their online education courses are as good as or superior to courses that use traditional, face-to-face instruction.

a. Give the null hypothesis for testing the claim made by the survey.

Short Answer

Expert verified

a. The null hypothesis is, \({H_0}:p = 0.74.\)

Step by step solution

01

Given Information

74% of college leaders believe that their online education courses are as good as or superior to courses that use traditional, face-to-face instruction.

02

State the large sample test of the hypothesis about p.

The test statistic used to obtaining the large sample test of the hypothesis about p is,

\({Z_c} = \frac{{\left( {\hat p - {p_0}} \right)}}{{{\sigma _{\hat p}}}}\)

The condition required for a valid large sample hypothesis test for p are:

  • The sample size n is large.
  • A random sample is selected from a binomial population.
03

State the null hypothesis of the test.

a.

Let p be the true proportion of college leaders who believe that their online education courses are as good as or superior to courses that use traditional, face-to-face instruction.

The value of the p is computed as:

\(\begin{aligned}p = \frac{{74}}{{100}}\\ = 0.74\end{aligned}\)

The required null hypothesis is,\({H_0}:p = 0.74.\)

Hence, the null hypothesis is that the true proportion of college leaders who believe that their online education courses are as good as or superior to courses that use traditional, face-to-face instruction is 0.74.

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Most popular questions from this chapter

Producer's and consumer's risk. In quality-control applications of hypothesis testing, the null and alternative hypotheses are frequently specified as\({H_0}\)The production process is performing satisfactorily. \({H_a}\): The process is performing in an unsatisfactory manner. Accordingly, \(\alpha \) is sometimes referred to as the producer's risk, while \(\beta \)is called the consumer's risk (Stevenson, Operations Management, 2014). An injection molder produces plastic golf tees. The process is designed to produce tees with a mean weight of .250 ounce. To investigate whether the injection molder is operating satisfactorily 40 tees were randomly sampled from the last hour's production. Their weights (in ounces) are listed in the following table.

a. Write \({H_0}\) and \({H_a}\) in terms of the true mean weight of the golf tees, \(\mu \).

b. Access the data and find \(\overline x \)and s.

c. Calculate the test statistic.

d. Find the p-value for the test.

e. Locate the rejection region for the test using\({H_a} = 0.01\).

f. Do the data provide sufficient evidence to conclude that the process is not operating satisfactorily?

g. In the context of this problem, explain why it makes sense to call \(\alpha \)the producer's risk and \(\beta \)the consumer's risk.

Stability of compounds in new drugs. Refer to the ACS Medicinal Chemistry Letters (Vol. 1, 2010) study of the metabolic stability of drugs, Exercise 2.22 (p. 83). Recall that two important values computed from the testing phase are the fraction of compound unbound to plasma (fup) and the fraction of compound unbound to microsomes (fumic). A key formula for assessing stability assumes that the fup/fumic ratio is 1:1. Pharmacologists at Pfizer Global Research and Development tested 416 drugs and reported the fup/fumic ratio for each. These data are saved in the FUP file, and summary statistics are provided in the accompanying Minitab printout. Suppose the pharmacologists want to determine if the true mean ratio, 渭, differs from 1.

a. Specify the null and alternative hypotheses for this test.

b. Descriptive statistics for the sample ratios are provided in the Minitab printout on page 410. Note that the sample mean,\(\overline x = .327\)is less than 1. Consequently, a pharmacologist wants to reject the null hypothesis. What are the problems with using such a decision rule?

c. Locate values of the test statistic and corresponding p-value on the printout.

d. Select a value of\(\alpha \)the probability of a Type I error. Interpret this value in the words of the problem.

e. Give the appropriate conclusion based on the results of parts c and d.

f. What conditions must be satisfied for the test results to be valid?

: A random sample of n = 200 observations from a binomial population yield

p^=0.29

a. Test H0:p=0.35 against H0:p<0.35. Usea=0.05.

a. List three factors that will increase the power of a test.

b. What is the relationship between b, the probability of committing a Type II error, and the power of a test?

Companies that produce candies typically offer different colors of their candies to provide consumers a choice. Presumably, the consumer will choose one color over another because of taste. Chance (Winter 2010) presented an experiment designed to test this taste theory. Students were blindfolded and then given a red or yellow Gummi Bear to chew. (Half the students were randomly assigned to receive the red Gummi Bear and half to receive the yellow Bear. The students could not see what color Gummi Bear they were given.) After chewing, the students were asked to guess the color of the candy based on the flavor. Of the 121 students who participated in the study, 97 correctly identified the color of the Gummi Bear.

a. If there is no relationship between color and Gummi Bear flavor, what proportion of the population of students would correctly identify the color?

b. Specify the null and alternative hypotheses for testing whether color and flavor are 伪=.01related.

c. Carry out the test and give the appropriate conclusion at Use the p-value of the test, shown on the accompanying SPSS printout, to make your decision.
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