Question

A survey in a large class for first-year college students asked, "About how many hours do you study during a typical week?" The mean response of the 461 students was

x = 15.3 hours.

Suppose that we know that the study time follows a Normal distribution with standard deviation

σ = 8.5 hours

for all first-year students at this university.

Does the survey results provide evidence (at the 0.05 level) of students claiming to study more than 15 hours per week on average?

(a) State null and alternative hypotheses in terms of the mean study time.

H₀: μ ≤ 15 hours
H₁: μ > 15 hoursH₀: μ < 15 hours
H₁: μ = 15 hours    H₀: μ = 15 hours
H₁: μ ≠ 15 hoursH₀: μ = 15 hours
H₁: μ < 15 hours

(b) What is the value of the test statistic z? (Give your answer to two decimal places.)

z =

(c) What is the P-value of the test?

less than 0.001between 0.001 and 0.01    between 0.01 and 0.025between 0.025 and 0.05larger than 0.05

(d) What can we conclude about students claiming to study more than 15 hours per week on average?

There is sufficient evidence that the average amount of time students claim to study is more than 15 hours per week.There is insufficient evidence that the average amount of time students claim to study is more than 15 hours per week.  

Answer 1