Question

The one-sample t statistic for a test of:

H0: μ = 50
Ha: μ < 50
based on n = 15 observations has the value t = -3.102.

Answer 1

To reject the null hypothesis in this one-sample t-test, we need to find the critical t value. Since the alternative hypothesis (Ha) is μ < 50, this is a left-tailed test. With a significance level of 0.05, we need to find the t value that has an area of 0.05 to the left.

Step-by-step explanation:

To reject the null hypothesis in this one-sample t-test, we need to find the critical t value. Since the alternative hypothesis (Ha) is μ < 50, this is a left-tailed test. With a significance level of 0.05, we need to find the t value that has an area of 0.05 to the left.

Using a t-table or statistical software, we find that for a left-tailed test with 14 degrees of freedom (n-1), the critical t value is approximately -1.761. Since the given t value of -3.102 is lower than the critical value, we reject the null hypothesis, concluding that there is evidence to suggest that the population mean is less than 50.