Question

R=8
please use z table for distribution question

A researcher claimed that the average age of nurses in City B is at most 39 years. The researcher interviewed a random sample of 49 nurses from City B. The average age of the selected nurses was 40+ years. It is known that the ages of nurses in City B follow a normal distribution with a standard deviation of 5 years. Test the claim of the researcher using a z test with critical value method at a level of significance of 0.017. (a) State the hypothesis and identify the claim. (2 marks) (b) Determine if the test is left-tailed, right-tailed or two-tailed and find the critical value. Correct your critical value to 2 decimal places, (2 marks) Find the test value. Correct your answer to 2 decimal places (2 marks) (d) Make a decision for the test. (2 marks) Summarize the result of the test. (2 marks)

Answer 1

$\mu$ = 39, $\bar{x}$ = 40.8, $\sigma$ = 5, n = 49, $\alpha$ = 0.017

Since the claim is that the mean age is at most, it means the null hypothesis will have the < sign.

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(a) The Hypothesis:

H0: $\mu$ < 39

Ha: $\mu$ > 39

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(b) This is a Right tailed test (as the alternative has a > sign)

The z critical at $\alpha$ = 0.017 is 2.39

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(c) The Test Statistic: The test statistic is given by the equation:

z = =" - 44 2.52

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(d) Since Z test is > z critical (2.39), We Reject the Null Hypothesis

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(e) The Conclusion: There is sufficient evidence at the 98.83% significance level to warrant rejection of the claim that the average age of nurses in City B is at most 39 years.

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