Question

In a study of cell phone usage and brain hemispheric dominance, an Internet survey was e-mailed to 6974 subjects randomly selected from an online group involved with ears. There were 1335 surveys returned. Use a 0.01 significance level to test the claim that the return rate is less than​ 20%. Use the​ P-value method and use the normal distribution as an approximation to the binomial distribution.

Identify the null hypothesis and alternative hypothesis.

A. H0​: p=0.2

H1​: p<0.2

B. H0​: p≠0.2

H1​: p=0.2

C. H0​: p= 0.2

H1​: p < 0.2

D. H0​: p = 0.2

H1​: p > 0.2

E. H0​: p > 0.2

H1​: p = 0.2

F. H0​: p = 0.2

H1​:p ≠ 0.2

The test statistic is z=

The P-Value is =

Because the​ P-value is ________ the significance level, ______ the null hypothesis. There is ______ evidence to support the claim that the return rate is less than​ 20%.

Answer 1

To test the claim that survey return rate is less than 20%, the correct hypothesis testing setup is H0: p=0.2 and Ha: p<0.2. We use the normal approximation to perform the test and compare the calculated p-value with the significance level of 0.01 to determine if we should reject the null hypothesis.

Step-by-step explanation:

To test the claim that the return rate of surveys is less than 20%, we need to identify the correct null hypothesis (H0) and alternative hypothesis (Ha). The correct hypotheses are A. H0: p=0.2 H1: p<0.2, where 'p' represents the population proportion of survey returns. We are testing if the true proportion is less than 20%, thus the alternative hypothesis is 'p<0.2'. The null hypothesis is the statement of no effect or no difference, essentially stating that the proportion is equal to 20%.

To perform the test, we use the normal distribution as an approximation to the binomial distribution because the sample size is large enough. The test statistic for a proportion is calculated using the formula: z = (p' - p) / sqrt(p(1-p)/n), where p' is the sample proportion, p is the hypothesized proportion, and n is the sample size. In this case, p' = 1335/6974. After calculating the test statistic, we compare the p-value to the significance level of 0.01. If the p-value is less than the significance level, we reject the null hypothesis and conclude there is evidence to support the claim.

Since the question does not provide the specific calculations for the test statistic or p-value for this scenario, we cannot complete the final step here. The interpretation depends on whether the p-value is above or below the significance level, with 'reject the null hypothesis' or 'do not reject the null hypothesis' and commenting on the evidence for the claim accordingly.