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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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Most popular questions from this chapter

Haemoglobin is a protein in red blood cells that carries oxygen from the lungs to body tissues. People with less than 12 grams of haemoglobin per deciliter of blood (g/dl) are anaemic. A public health official in Jordan suspects that Jordanian children are at risk of anaemia. He measures a random sample of 50 children.

Anemia For the study of Jordanian children in Exercise 64, the sample mean hemoglobin level was 11.3mg/dl and the sample standard deviation was 1.6mg/dl.

(a) Calculate the test statistic.

(b) Find the P-value using Table B. Then obtain a

more precise P-value from your calculator.

Pressing pills A drug manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The hardness of a sample from each batch of tablets produced is measured to control the compression process. The target value for the hardness is 渭=11.5. The hardness data for a random sample of 20tablets are

11.62711.61311.49311.60211.36011.37411.59211.45811.55211.46311.38311.71511.48511.50911.42911.47711.57011.62311.47211.531

Is there significant evidence at the5% level that the mean hardness of the tablets differs from the target value? Carry out an appropriate support your answer.

Which of the following 95% confidence intervals would lead us to reject H0:p=0.30in favor of Ha:p鈮�0.30at the 5% significance level?

(a) (0.29, 0.38) (c) (0.27, 0.31) (e) None of these

(b) (0.19, 0.27) (d) (0.24, 0.30)

A local high school makes a change that should improve student satisfaction with the parking situation. Before the change, 37% of the school鈥檚 students approved of the parking that was provided. After the change, the principal surveys an SRS of 200 of the over 2500 students at the school. In all, 83 students say that they approve of the new parking arrangement. The principal cites this as evidence that the change was effective. Perform a test of the principal鈥檚 claim at the 伪=0.05 significance level.
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