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Chapter 9: Q.51 (page 564)

(a) Construct and interpret a 95% confidence interval for the proportion of all teens in the state who passed their driving test on the first attempt.

(b) Explain what the interval in part (a) tells you about the DMV's claim.

Short Answer

Expert verified

a. The confidence interval is(0.607,0.769)

b. It is an incorrect claim

Step by step solution

01

Introduction

A confidence interval is the mean of your estimate in addition to and minus the variation in that estimate. This is the scope of values you anticipate that your estimate should fall between if you re-try your test, within a certain degree of confidence. Confidence, in statistics, is one more method for describing probability.

02

Explanation Part (a)

The number of teens is n =125

The number of teens that passed a test x = 86

population proportion = 60%=0.6

p-=xn=86125=0.688

Using,

CI=p-±zα/2×p-(1−p-)n

CI=0.688±1.960×0.688(1-0.688)125

CI=(0.607,0.769)

03

Explanation Part (b)

We know that 0.60doesn't lie in the confidence interval. Hence, It is an incorrect claim.

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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.

According to the Web site sleepdeprivation.com, 85% of teens are getting less than

eight hours of sleep a night. Jannie wonders whether this result holds in her large high school. She asks an SRS of 100 students at the school how much sleep they get on a typical night. In all, 75 of the responders said less than 8 hours.

(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—H0:μ=6.7versusHa:μ<6.7 or the one from part (a) of this exercise—would you be

more interested in? Justify your answer.

Write a few sentences comparing what the P-values in Exercises 13 and 14 tell you about statistical significance in each of the two studies.

In planning a study of the birth weights of babies whose mothers did not see a doctor

before delivery, a researcher states the hypotheses as

H0:x¯=1000gramsHa:x¯<1000grams
See all solutions

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