Question

A random sample of 25 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 11 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 10.5.

Is it appropriate to use a Student's t distribution? Explain.
a. Yes, because the x distribution is mound-shaped and symmetric and σ is unknown.
b. No, the x distribution is skewed left.
c. No, the x distribution is skewed right.
d. No, the x distribution is not symmetric.
e. No, σ is known.

Answer 1

The appropriate distribution to use for the hypothesis test in this scenario would be the Student's t-distribution, as the sample is drawn from a mound-shaped and symmetric distribution. The sample standard deviation is used as an estimate for the population standard deviation.

Step-by-step explanation:

The appropriate distribution to use for the hypothesis test in this scenario would be the Student's t-distribution. This is because the sample is drawn from a mound-shaped and symmetric distribution, which satisfies the assumption of normality. Additionally, the population standard deviation is unknown, so the sample standard deviation is used as an estimate. The level of significance of 0.05 indicates that we are conducting a two-tailed test.

To perform the test, we can calculate the t-value using the formula:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

Once we have the t-value, we can compare it to the critical values from the t-distribution table to determine if we reject the null hypothesis or not.