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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:渭=150H1:渭<150

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

Using

t=x炉鈭�渭sx/n~tn鈭�1

role="math" localid="1652944541809" t=137鈭�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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Most popular questions from this chapter

You are testing HO:渭=10H伪:渭<10against based on an SRS of 20observations from a Normal population. The tstatistic is . t=-2.25The P-value

(a) falls between 0.01and0.02

(b) falls between0.02and0.04

(c) falls between0.04and0.05

(d) falls between .05and0.25.

(c) is greater than0.25.

The power of tomatoes The researchers who carried out the experiment in Exercise 75suspect that the large P-value (0.114) is due to low power.

(a) Describe a Type I and a Type II error in this setting. Which type of error could you have made in Exercise 75? Why?

(b) Explain two ways that the researchers could have increased the power of the test to detect .

(a) State hypotheses for a significance test to determine whether first responders are arriving within 8 minutes of the call more often. Be sure to define the parameter of interest.

(b) Describe a Type I error and a Type II error in this setting and explain the consequences of each.

(c) Which is more serious in this setting: a Type I error or a Type II error? Justify your answer.

(d) If you sustain a life-threatening injury due to a vehicle accident, you want to receive medical treatment as quickly as possible. Which of the two significance tests鈥�H0:渭=6.7versusHa:渭<6.7 or the one from part (a) of this exercise鈥攚ould you be

more interested in? Justify your answer.

As part of its 2010 census marketing campaign, the U.S. Census Bureau advertised

鈥�10 questions, 10 minutes鈥攖hat鈥檚 all it takes.鈥� On the census form itself, we read, 鈥淭he

U.S. Census Bureau estimates that, for the average household, this form will take

about 10 minutes to complete, including the time for reviewing the instructions and

answers.鈥� We suspect that the actual time it takes to complete the form may be longer

than advertised.

Healthy bones The recommended daily allowance (RDA) of calcium for women between the ages of 18and 24years is 1200milligrams (mg). Researchers who were involved in a large-scale study of women鈥檚 bone health suspected that their participants had significantly lower calcium intakes than the RDA. To test this suspicion, the researchers measured the daily calcium intake of a random sample of 36women from the study who fell in the desired age range. The Minitab output below displays descriptive statistics for these data, along with the results of a significance test.

(a) Determine whether there are any outliers. Show your work.

(b) Interpret the P-value in context.

(c) Do these data give convincing evidence to support the researchers鈥� suspicion? Carry out a test pg 571to help you answer this question.
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