Explanation Calculation: It is given that the sample size n = 65 , sample mean x ¯ = 38.16 and the population standard deviation σ = 5.95 . In this context, the parameter of interest is population mean. Because the researcher interested to test the population mean. However, the value of σ is known, so, the z -test is appropriate. Assumptions for performing a hypothesis test about μ when σ is known: • The samples taken from the population are simple random samples. • The sample size should be large that is, n > 30 or the population should be distributed normally. Requirement check: • The sample of 65 was selected at random. • The sample size of 65 is greater than 30, that is, 65 > 30 . Thus, the condition is satisfied. Step 1: Denote μ as true population mean. The test hypotheses are given below: Null hypothesis: H 0 : μ = 40 That is, the true population mean is 40 . Alternative hypothesis: H 1 : μ < 40 That is, the true population mean is less than 40 . Step 2: It is given that the level of significance is 0.01. Step 3: Test statistic: The t- test statistic is: t = x ¯ − μ σ n , Where, x ¯ be the sample mean, μ be the hypothesized mean and σ be the standard deviation and n be the sample size

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ISBN: 9781259570643

Author: Navidi

Publisher: MCG

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Chapter 8.5, Problem 4CYU

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Identify the parameter of interest.

Check whether it can be concluded that the population mean is less than 40 at the level of significance α=0.01.

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Identify the parameter of interest. Check whether it can be concluded that the population mean is less than 40 at the level of significance α=0.01.

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Identify the parameter of interest.

Check whether it can be concluded that the population mean is less than 40 at the level of significance α=0.01.