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Chapter 9: Q.76 (page 589)

A student group claims that first-year students at a university study 2.5 hours per night during the school week. A skeptic suspects that they study less than that on average. He takes a random sample of 30 first-year students and finds that x-=137 minutes and sx=45 minutes. A graph of the data shows no outliers but some skewness. Carry out an appropriate significance test at the 5% significance level. What conclusion do you draw?

Short Answer

Expert verified

The students in the university on an average study2.5hours on an average night.

Step by step solution

01

Introduction 

The significance level of an occasion (like a statistical test) is the probability that the occasion might have happened by some coincidence. If the level is quite low, that is to say, the probability of occurring by chance is tiny, we say the occasion is significant.

02

Explanation

Calculating the null and alternative hypotheses,

H0:μ=150H1:μ<150

Now, role="math" localid="1652944307124" x-=137sx=45n=30

Using

t=x¯−μsx/n~tn−1

role="math" localid="1652944541809" t=137−15045/30=-1.582

At the significance level 0.05the critical value is-1.699

If the critical value is less than the t value the null hypothesis is not rejected.

Hence we can conclude that students in the university an average study2.5 hours on an average night.

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