Question

According to a​ magazine, people read an average of more than three books in a month. A survey of 20 random individuals found that the mean number of books they read was 3.2 with a standard deviation of 1.24. a. To test the​ magazine's claim, what should the appropriate hypotheses​ be? b. Compute the test statistic. c. Using a level of significance of​ 0.05, what is the critical​ value? d. Find the​ p-value for the test. e. What is your​ conclusion? Question content area bottom Part 1 a. To test the​ magazine's claim, what should the appropriate hypotheses​ be? Determine the null​ hypothesis, H0​, and the alternative​ hypothesis, H1. H0​: ▼ piπ sigmaσ muμ ▼ less than< equals= greater than> not equals≠ less than or equals≤ greater than or equals≥ enter your response here H1​: ▼ muμ sigmaσ piπ ▼ greater than or equals≥ less than or equals≤ less than< equals= not equals≠ greater than> enter your response here ​(Type whole​ numbers.) Part 2 b. Compute the test statistic. enter your response here ​(Round to two decimal places as​ needed.) Part 3 c. Using a level of significance of​ 0.05, what is the critical​ value? enter your response here ​(Round to two decimal places as​ needed.) Part 4 d. Find the​ p-value for the test. enter your response here ​(Round to three decimal places as​ needed.) Part 5 e. What is your​ conclusion? The​ p-value is ▼ greater than less than the chosen value of α​, so ▼ do not reject reject the null hypothesis. There is ▼ sufficient insufficient evidence to conclude that mean is greater than 3.

Answer 1

a. H0: μ ≤ 3 (Null hypothesis)

H1: μ > 3 (Alternative hypothesis)

b. Test statistic = 1.29

c. Critical value = 1.729

d. P-value ≈ 0.102

e. The p-value is greater than the chosen value of α, so we do not reject the null hypothesis. There is insufficient evidence to conclude that the mean is greater than 3.

Step-by-step explanation:

a. To test whether the claim that people read more than three books on average holds, the null hypothesis (H0) states that the mean number of books read (μ) is less than or equal to 3. The alternative hypothesis (H1) suggests that the mean number of books read is greater than 3.

b. The test statistic, calculated using the formula

Test statistic = Sample mean − Population mean / Standard deviation / √Sample size , is 1.29. This value indicates how many standard deviations the sample mean is away from the population mean.

c. With a significance level (α) of 0.05 for a one-tailed test, the critical value for rejecting the null hypothesis lies at 1.729, obtained from the z-table or a statistical calculator.

d. The calculated p-value is approximately 0.102. This value represents the probability, under the assumption that the null hypothesis is true, of observing a sample mean as extreme as the one obtained or more extreme. Since the p-value is greater than α (0.05), we fail to reject the null hypothesis.

In summary, based on the given data and using a significance level of 0.05, we do not have sufficient evidence to conclude that the mean number of books read per month is greater than 3. The p-value suggests that the observed sample mean is not significantly different from the claimed average of more than three books per month, thus failing to reject the null hypothesis.