Question

 Determine the direction of the hypothesis test (one-sided left, one-sided right, bidirectional)
 Determine the test statistic (z* or t*) and the p-value for each of the following situations and
 Determine if they would cause the rejection of the null hypothesis if the confidence level was set
at 95% in each case. (Hint: be wary of the sample size)

Ho: μ = 380 s, Ha: μ ≠ 380 s, sample mean = 357, s = 75, n = 40

Answer 1

Answer on Question #60778 – Math – Statistics and Probability

Question

- Determine the direction of the hypothesis test (one-sided left, one-sided right, bidirectional)

- Determine the test statistic (z* or t*) and the p-value for each of the following situations and

- Determine if they would cause the rejection of the null hypothesis if the confidence level was set

at 95% in each case. (Hint: be wary of the sample size)

Ho: μ = 380 s, Ha: μ ≠ 380 s, sample mean = 357, s = 75, n = 40

Solution

- Since the alternative hypothesis contains “≠” statement, the test is bidirectional.

- Since the sample size is large (n ≥ 30), one can use z-test and use s as a point estimate of σ.

The test statistic:

$$\begin{array}{l} z = \frac {\bar {x} - \mu}{s / \sqrt {n}}; \\ z = \frac {357 - 380}{75 / \sqrt {40}} = -1.94. \end{array}$$

The critical values can be either obtained from the standard normal table or calculated using the technology (NORM.S.INV() function of MS Excel).

For two-tailed test with α = 0.05, the critical values are zc = ±1.96.

The rejection region: |z| > 1.96.

- Since the test statistic does not fall within the rejection region, fail to reject the null hypothesis at the given confidence level (95%).

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