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Chapter 9: Q. 35 (page 394)

The normal probability curve and stem-to-leaf diagram of the data are shown in figure; 蟽is unknown.

Perform Hypothesis test for mean of the population from which data is obtained and decide whether to use z-test, t-test or neither. Explain your answer.

Short Answer

Expert verified

Neither test is used.

Step by step solution

01

Step 1. Given Information 

02

Step 2. Conditions to use z-test

Small Sample size:

If the sample size is less than 15, the z-test procedure is used when the variable is normally distributed or very close to being normally distributed.

Moderate Sample size:

If the sample size lies between 15 and 30, the z- test procedure is used when the variable far from being normally distributed or there is no outlier in the data.

Large Sample size:

If the sample size is greater than 30, the z- test procedure is used without any restriction.

03

Step 3. Conditions for t-test

Small Sample size:

  • Samples are randomly selected from the population.
  • Population follows normal distribution or the sample size is larger.
  • The standard deviation is unknown.
04

Step 4. Explanation 

Here, the sample is selected from the population and the sample size is small. Moreover, the distribution of the variable is not normally distributed. Hence, neither test is used for given scenario.

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Most popular questions from this chapter

Serving Time. According to the Bureau of Crime Statistics and Research of Australia, as reported on Lawlink, the mean length of imprisonment for motor-vehicle theft offenders in Australia is 16.7 months. One hundred randomly selected motor-vehicle-theft offenders in Sydney, Australia, had a mean length of imprisonment of 17.8 months. At the5% significance level, do the data provide sufficient evidence to conclude that the mean length of imprisonment for motor-vehicle theft offenders in Sydney differs from the national mean in Australia? Assume that the population standard deviation of the lengths of imprisonment for motor-vehicle-theft offenders in Sydney is 6.0 months.

Dementia is the loss of the in actual and social abilities severe enough to interfere with judging behavior and daily functioning. Alzheimer's disease is the most common type of dementia. In the article "Living with Early Onsite dementia: Exploring the Experience and Developing Evidence Guidelines for Practice", P Harris and J Keady explored the experiment struggles of people diagnosed with dementia and their familiar simple random sample \(21\) people with early-onset dementia the following data on age at diagnosis in years.

At the \(1%\) significance level, do the data provide sufficient evidence to conclude that the mean age at diagnosis of all people with early onset dementia is less than \(55\) years old? Assume that the population is standard deviation is \(6.8\) years.

In Exercise 8.146 on page 345,we introduced one-sided one mean-t-intervals. The following relationship holds between hypothesis test and confidence intervals for one-mean t-procedures: For a right-tailed hypothesis test at the significance level 伪, the null hypothesis H0:渭=渭0will be rejected in favor of the alternative hypothesis data-custom-editor="chemistry" Ha:渭>渭0if and only if 渭0is less than or equal to the 1-伪-level lower confidence bound for 渭. In each case, illustrate the preceding relationship by obtaining the appropriate lower confidence bound and comparing the result to the conclusion of the hypothesis test in the specified exercise.

Part (a): Exercise 9.114 (both parts)

Part (b) Exercise9.115

As we mentioned on page \(378\), the following relationship holds between hypothesis tests and confidence intervals for one mean \(z-\)procedures: For a two-tailed hypothesis test at the significance level \(\alpha\), the null hypothesis \(H_{0}:\mu =\mu_{0}\) will be rejected in favor of the alternative hypothesis \(H_{a}:\mu \neq \mu_{0}\) if and only if \(\mu_{0}\) lies outside the \((1-\infty)\) level confidence interval for \(\mu\). In each case, illustrate the preceding relationship by obtaining the appropriate one-mean \(z-\)interval and comparing the result to the conclusion of the hypothesis test in the specified exercise.

a. Exercise \(9.84\)

b. Exercise \(9.87\)

The following relationship holds between hypothesis tests and confidence intervals for one-mean t-procedures: For a two-tailed hypothesis test at the significance level 伪, the null hypothesis H0:渭=渭0will be rejected in favor of the alternative hypothesis Ha:渭>渭0if and only if 渭0lies outside the 1-伪-level confidence interval for 渭. In each case, illustrate the preceding relationship by obtaining the appropriate one-mean t-interval and comparing the result to the conclusion of the hypothesis test in the specified exercise.

Part (a): Exercise 9.113

Part (b): Exercise 9.116
See all solutions

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