Explanation Calculation: It is given that the sample size n = 65 , sample mean x ¯ = 57.3 and the population standard deviation σ = 12.6 . In this context, the parameter of interest is population mean, as the researcher is interested to test the population mean. Here, 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 = 60 That is, the true population mean is 60 . Alternative hypothesis: H 1 : μ < 60 That is, the true population mean is less than 60 . Step 2: It is given that the level of significance is 0.05. Step 3: Test statistic: The z- test statistic is: z = 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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Chapter 8.5, Problem 6E

To determine

Identify the parameter of interest.

Check whether it can be concluded that the population mean is less than 60 at the level of significance α=0.05.

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Chapter 8.5, Problem 5E

Chapter 8.5, Problem 7E

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Ch. 8.1 - Check Your Understanding 1. Last year, the mean...Ch. 8.1 - Prob. 2CYU Ch. 8.1 - Prob. 3CYU Ch. 8.1 - Prob. 4CYU Ch. 8.1 - Prob. 5CYU Ch. 8.1 - Prob. 6CYU Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - In Exercises 9–12, determine whether the statement...

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Identify the parameter of interest. Check whether it can be concluded that the population mean is less than 60 at the level of significance α = 0.05 .

Identify the parameter of interest. Check whether it can be concluded that the population mean is less than 60 at the level of significance α=0.05.

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Identify the parameter of interest.

Check whether it can be concluded that the population mean is less than 60 at the level of significance α=0.05.