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Chapter 9: Q 2.1. (page 570)

A college professor suspects that students at his school are getting less than 8 hours of sleep a night, on average. To test his belief, the professor asks a random sample of 28 students, 鈥淗ow much sleep did you get last night?鈥� Here are the data (in hours): 96868866.56794345611636610784.5977

Do these data provide convincing evidence in support of the professor鈥檚 suspicion? Carry out a significance test at the a=0.05level to help answer this question.

Short Answer

Expert verified

Yes, there is sufficient evidence to support the suspicion of professor.

Step by step solution

01

Given information

The data set is:96868866.56794345611636610784.5977

02

Concept

The test statistic is computed as: t=x鈭�渭sn

x=Sample mean

渭=Population mean

n= Sample size

s= Sample standard deviation

03

Calculation

Here,

be the average sleeping hours.

The null and alternative hypotheses are:H0:渭=8Ha:渭<8

The obtained excel output is:

Here, the p-value is 0.0006 Here, is the p-value.

Thus, at a 5% significance level, there is sufficient evidence to support the suspicion of the professor.

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