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Chapter 9: Q.35 (page 562)

Explain why we aren't safe carrying out a one-sample z test for the population proportion p.

You toss a coin 10 times to test the hypothesis H0:p=0.5 that the coin is balanced.

Short Answer

Expert verified

we aren't safe carrying out a one-sample z test for the population proportion p as the success and failures are not larger than ten.

Step by step solution

01

Introduction

The null hypothesis is a commonplace factual hypothesis which recommends that no factual relationship and importance exists in a bunch of given single noticed variables, between two arrangements of noticed information and estimated peculiarities.

02

Explanation

The sample size n =100

The hypothesis is

Using the number of success = np

=10脳0.5=5

The number of failures = n(1-p)

=10脳(1-0.5)=5

Hence we aren't safe carrying out a one-sample z test for the population proportion p as the success and failures are not larger than ten.

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Most popular questions from this chapter

The design of controls and instruments affects how easily people can use them. A student project investigated this effect by asking 25right-handed students to turn a knob (with their right hands) that moved an indicator. There were two identical instruments, one with a right-hand thread (the knob turns clockwise) and the other with a left-hand thread (the knob must be turned counterclockwise). Each of the 25students used both instruments in a random order. The following table gives the times in seconds each subject took to move the indicator a fixed distance:

(a) Explain why it was important to randomly assign the order in which each subject used the two knobs.

(b) The project designers hoped to show that right-handed people find right-hand threads easier to use. Carry out a significance test at the 5%significance level to investigate this claim

The most important condition for sound conclusions from statistical inference is that

(a) the data come from a well-designed random sample or randomized experiment

(b) the population distribution be exactly Normal.

(c) the data contain no outliers.

(d) the sample size be no more than 10%of the population size.

(c) the sample size be at least 30.

Sweetening colas Cola makers test new recipes for loss of sweetness during storage. Trained tasters rate the sweetness before and after storage. From experience, the population distribution of sweetness losses will be close to Normal. Here are the sweetness losses (sweetness before storage minus sweetness after storage) found by tasters from a random sample of 10batches of a new cola recipe:

2.00.40.72.0-0.42.2-1.31.21.12.3

Are these data good evidence that the cola lost sweetness? Carry out a test to help you answer this question.

(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.

Two-sided test The one-sample t statistic from a sample of n=25observations for the two-sided test of H0:渭=64;Ha:渭鈮�64has the value t=-1.12.

(a) Find the P-value for this test using (i) Table Band (ii) your calculator. What conclusion would you draw at the 5%significance level? At the 1%significance level?

(b) Redo part (a) using an alternative hypothesis of Ha:渭<64.
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