Question

A random sample of 100 observations from a quantitative population produced a sample mean of 21.5 and a sample standard deviation of 8.2. Use the p-value approach to determine whether the population mean is different from 23. Explain your conclusions. (Use α = 0.05.) State the null and alternative hypotheses. H0: μ = 23 versus Ha: μ < 23 H0: μ = 23 versus Ha: μ > 23 H0: μ = 23 versus Ha: μ ≠ 23 H0: μ < 23 versus Ha: μ > 23 H0: μ ≠ 23 versus Ha: μ = 23 Find the test statistic and the p-value. (Round your test statistic to two decimal places and your p-value to four decimal places.) z = p-value = State your conclusion. The p-value is greater than alpha, so H0 is not rejected. There is sufficient evidence to indicate that the mean is different from 23. The p-value is less than alpha, so H0 is rejected. There is sufficient evidence to indicate that the mean is different from 23. The p-value is greater than alpha, so H0 is not rejected. There is insufficient evidence to indicate that the mean is different from 23. The p-value is less than alpha, so H0 is rejected. There is insufficient evidence to indicate that the mean is different from 23. You may need to use the appropriate appendix table or technology to answer this question.

Answer 1

H₀: = 23

H₁: 23

The test statistic z = ()/(/)

                             = (21.5 - 23)/(8.2/)

                             = -1.83

P-value = 2 * P(Z < -1.83)

             = 2 * 0.0336

             = 0.0672

The P-value is greater than , so H₀ is not rejected. There is insufficient evidence to indicate that the mean is different from 23.