Question

1. Consider the following hypothesis test: Ho : μ = 15 H1 : μ ≠ 15 A sample of 50 provided a sample mean of 15.15. The population standard deviation is 3. a. Compute the value of the test statistic. b. What is the p value? c. At α = 0.05, what is the rejection rule using the critical value? What is your conclusion?

2. Consider the following hypothesis test: Ho: μ ≤ 51 H1: μ > 51 A sample of 60 is used and the population standard deviation is 8. Use α=0.05. a. Z critical = _______________ b. Sample mean = 53.5, z calc = ______________. Do you reject Ho? c. Sample mean = 51.8, z calc = ______________. Do you reject Ho? d. The Pvalue for c is:_________________

Answer 1

1)

Sample size = n = 50

Sample mean = = 15.15

Population standard deviation = = 3

The null and alternative hypothesis is

Ho : μ = 15 H1 : μ ≠ 15

Level of significance = 0.05

Here population standard deviation is known so we have to use z-test statistic.

Test statistic is

Critical value = 1.96    ( Using z table)

Critical value > Test statistic z we fail to reject the null hypothesis.

Conclusion: The population mean is 15.

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2)

Sample size = n = 60

Sample mean = = 53.5

Population standard deviation = = 8

The null and alternative hypothesis is

Ho: μ ≤ 51 H1: μ > 51

Level of significance = 0.05

Here population standard deviation is known so we have to use z-test statistic.

Test statistic is

Critical value = 1.64 ( Using z table)

Critical value < Test statistic z we reject the null hypothesis.

P-value = P(Z > 2.42) = 1 - P(Z < 2.42) = 1 - 0.9923 = 0.0077

Conclusion: The population mean is greater than 51.