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Chapter 9: Q.37 (page 562)

Lefties Refer to Exercise 33. In Simon's SRS, 16 of the students were left-handed.

(a) Calculate the test statistic.

(b) Find the P-value using Table A. Show this result as an area under a standard Normal curve,

Short Answer

Expert verified

a.1.23

b.0.218

Step by step solution

01

Introduction

The normal distribution is a consistent likelihood appropriation that is balanced on the two sides of the mean, so the right half of the middle is a perfect representation of the left side. The region under the ordinary dissemination bend addresses likelihood and the absolute region under the bend aggregates to one.

02

Explanation Part (a)

The sample size is n = 100

The number of left-handed students is x = 16

Population proportion is p = 12%=0.12

sample proportion p-=xn=16100=0.16

calculating the null and alternative hypotheses,

H0:p=0.12Ha:p鈮�0.12

Using the formula,

z=p-鈭�p0p01鈭�p0n

=0.16鈭�0.120.12(1鈭�0.12)100=1.23

03

Explanation Part (b)

The p-value is calculated as,

=2脳P(Z>|Z|)

=2脳P(Z>|1.23|)

=2脳0.109=0.218

The standard normal curve is,

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Most popular questions from this chapter

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.

In a test of H0:p=0.4against Ha:p鈮�0.4, a random sample of size 100yields a test statistic of z=1.28. The P-value of the test is approximately equal to

(a) 0.90.

(b) 0.40.

(c) 0.05.

(d) 0.20.

(e) 0.10.

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)

When asked to explain the meaning of the P-value in Exercise 13, a student

says, 鈥淭his means there is only probability 0.01 that the null hypothesis is true.鈥� Explain clearly why the student鈥檚 explanation is wrong.

A blogger claims that U.S. adults drink an average of five 8-ounce glasses of water per day. Skeptical researchers ask a random sample of 24 U.S. adults about their daily water intake. A graph of the data shows a roughly symmetric shape with no outliers. The figure below displays Minitab output for a one-sample t interval for the population mean. Is there convincing evidence at the 10%significance level that the blogger鈥檚 claim is incorrect? Use the confidence interval to justify your answer.
See all solutions

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