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Chapter 9: Q.1.1 Check your understanding (page 555)

According to the National Campaign to Prevent Teen and Unplanned Pregnancy, 20% of teens aged 13 to 19 say that they have electronically sent or posted sexually suggestive images of themselves. 'The counsellor at a large high school worries that the actual figure might be higher at her school. To find out, she gives an anonymous survey to a random sample of 250 of the school's 2800 students. All 250 respond and 63 admit to sending or posting sexual images. Carry out a significance test at the 伪=0.05 significance level. What conclusion should the counsellor draw?

Short Answer

Expert verified

The conclusion is that the actual figure is higher than assumed before

Step by step solution

01

Introduction

Teen pregnancy is the point at which a lady under twenty gets pregnant. It ordinarily alludes to adolescents between the ages of 15-19. However, it can incorporate young ladies as youthful as ten. It's likewise called juvenile pregnancy.

02

Explanation

Given,

Sample size n is 250and Confidence level is 95%

Significance level 伪=0.05and population proportion is 0.20

Calculating the null and alternative hypotheses,

H0:p=0.20Ha:p>0.20

Using,

role="math" localid="1652858782146" z=p^鈭�p0p01鈭�p0n=0.252-0.0190.019(1-0.019)250=2.055

Hence the conclusion is that the actual figure is higher than assumed before

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Most popular questions from this chapter

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.

Are TV commercials louder than their surrounding programs? To find out, researchers collected data on 50randomly selected commercials in a given week. With the television鈥檚 volume at a fixed setting, they measured the maximum loudness of each commercial and the maximum loudness in the first 30seconds of regular programming that followed. Assuming conditions for inference are met, the most appropriate method for answering the question of interest is

(a) a one-proportion z test.

(b) a one-proportion z interval.

(c) a paired t test.

Significance and sample size A study with 5000 subjects reported a result that was statistically significant at the 5% level. Explain why this result might not be particularly large or important.

The reason we use tprocedures instead of zprocedures when carrying out a test about a population mean is that

(a) zcan be used only for large samples.

(b)zrequires that you know the population standard deviation 蟽.

(c) zrequires you to regard your data as an SRS from the population.

(d) zapplies only if the population distribution is perfectly Normal.

(e) zcan be used only for confidence intervals.

You are thinking about opening a restaurant and are searching for a good location. From the research you have done, you know that the mean income of those living near the restaurant must be over $85,000 to support the type of upscale restaurant you wish to open. You decide to take a simple random sample of 50 people living near one potential location. Based on the mean income of this sample, you will decide whether to open a restaurant there.8

(a) State appropriate null and alternative hypotheses. Be sure to define your parameter.

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

(c) If you had to choose one of the 鈥渟tandard鈥� significance levels for your significance test, would you choose 伪=0.01, 0.05, or 0.10? Justify your choice.
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