To find the p-value for this hypothesis test, we first need to calculate the test statistic. This is a one-sample z-test, because we're comparing a sample mean to a population mean, and we know the population standard deviation.

Step 1: State the null and alternative hypotheses. The null hypothesis (H0) is that the average debt load of graduating students with a bachelor’s degree is equal to $15,800. The alternative hypothesis (H1) is that the average debt load is not equal to $15,800.

Step 2: Calculate the test statistic. The formula for the z-score is:

Z = (X̄ - μ) / (σ/√n)

where:
X̄ = sample mean = $17,000
μ = population mean = $15,800
σ = population standard deviation = $4,320
n = sample size = 35

Substituting the values into the formula, we get:

Z = ($17,000 - $15,800) / ($4,320/√35) ≈ 1.63

Step 3: Find the p-value. The p-value is the probability that you would observe a more extreme test statistic in the direction of the alternative hypothesis if the null hypothesis were true. Since this is a two-tailed test (because the alternative hypothesis is that the average debt load is not equal to $15,800), we need to find the two-tailed p-value.

Looking up the z-score of 1.63 in a standard normal (Z) table or using a Z to P calculator, we find that the one-tailed p-value is approximately 0.0514. Because this is a two-tailed test, we double this value to get the two-tailed p-value.

So, the p-value for this hypothesis test is approximately 0.1028.

Question

To find the p-value for this hypothesis test, we first need to calculate the test statistic. This is a one-sample z-test, because we're comparing a sample mean to a population mean, and we know the population standard deviation.

Step 1: State the null and alternative hypotheses. The null hypothesis (H0) is that the average debt load of graduating students with a bachelor’s degree is equal to $15,800. The alternative hypothesis (H1) is that the average debt load is not equal to $15,800.

Step 2: Calculate the test statistic. The formula for the z-score is:

Z = (X̄ - μ) / (σ/√n)

where:
X̄ = sample mean = $17,000
μ = population mean = $15,800
σ = population standard deviation = $4,320
n = sample size = 35

Substituting the values into the formula, we get:

Z = ($17,000 - $15,800) / ($4,320/√35) ≈ 1.63

Step 3: Find the p-value. The p-value is the probability that you would observe a more extreme test statistic in the direction of the alternative hypothesis if the null hypothesis were true. Since this is a two-tailed test (because the alternative hypothesis is that the average debt load is not equal to $15,800), we need to find the two-tailed p-value.

Looking up the z-score of 1.63 in a standard normal (Z) table or using a Z to P calculator, we find that the one-tailed p-value is approximately 0.0514. Because this is a two-tailed test, we double this value to get the two-tailed p-value.

So, the p-value for this hypothesis test is approximately 0.1028.

Knowee AI · Accepted Answer