Please I need help with this question: A student group claims that first-year st

Question

Please I need help with this question: A student group claims that first-year students at a university must study 2.5 hours per night during the school week. A skeptic suspects that they study less than that on the average. A class survey finds that the average study time claimed by 269 students is x = 137 minutes. Regard these students as a random sample of all first-year students and suppose we know that study times follow a Normal distribution with standard deviation 65 minutes. Carry out a test of H0: µ 150 Ha: µ < 150. What do you conclude at the 10% significance level?

Explanation / Answer

Solution

µ = average study time for all first-year students at this university.
State hypotheses:
H0 : µ 150 min
Ha : µ < 150 min.
Test statistic z* = xµ0//n = 137150/65/269 = 3.28
P-value P(Z < z) = P(Z < 3.28) = 0.0005.
significance level = 10% = 0.10
Conclusion: p-value < 0.10 so reject null hypothesis.
This is very strong evidence that students study less than 2.5 hours per night

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