Question

Suppose that you are to conduct the following hypothesis test:

H0:H1:μ μ=≠510510H0:μ=510H1:μ≠510

Assume that you know that σ=90σ=90, n=42n=42, x=487.5x¯=487.5, and take α=0.1α=0.1. Draw the sampling distribution, and use it to determine

A. The value of the standardized test statistic:

Answer 1

The provided information enables us to perform a z-test using the known population standard deviation, sample size, sample mean, and significance level. By calculating the z-score, we will determine whether to reject or fail to reject the null hypothesis in this hypothesis testing scenario.

Step-by-step explanation:

The student has been asked to conduct a hypothesis test involving a single population mean μ, and to calculate the value of the standardized test statistic. The null hypothesis H0 states that μ = 510, while the alternative hypothesis H1 states that μ ≠ 510. With a known population standard deviation (σ = 90), sample size (n = 42), sample mean (μ = 487.5), and level of significance (α = 0.1), we can use the normal distribution to perform a z-test.

To find the standardized test statistic, also known as the z-score, we use the formula:

z = (μ - μ0) / (σ / √n)

Plugging in the values, we get:

z = (487.5 - 510) / (90 / √42)

Calculating this, we arrive at the z-score that is used to determine whether we should fail to reject or reject the null hypothesis based on the comparison with critical z-values corresponding to the significance level α.