Question

andomly selected college students is listed below. Complete the following hypothesis test: H0​:μ=7,Ha​:μ<7,α=0.05. (a) Find t. (Give your answer correct to two decimal places.) (ii) Find the p-value. (Give your answer correct to four decimal places.)

Answer 1

In this hypothesis test, we need to find 't' and the p-value given the significance level α. We calculate 't' using the t-distribution and compare it with the critical value to determine the p-value.

Step-by-step explanation:

The given hypothesis test is H0: μ = 7 and Ha: μ < 7. The significance level, α, is 0.05. To find t, we need to calculate it using the given information. To find the p-value, we can use the t-distribution table or a calculator.

1. Calculating t: Since the population standard deviation is not given, we assume it to be unknown and use the t-distribution. Considering the sample size and degrees of freedom, we find the critical value for one-tailed test at α = 0.05 to be -1.7141 (rounded to two decimal places).
2. Calculating p-value: To find the p-value, we compare the t-value with the critical value. The t-value is calculated by (sample mean - population mean)/(sample standard deviation/sqrt(sample size)). If the t-value is less than the critical value, the p-value is less than α, and we reject the null hypothesis.