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Chapter 9: Q. 37 (page 394)

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

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 used

Step by step solution

01

Step 1. Given Information 

02

Step 2. Conditions to use z-test

Small Sample size:

For sample size 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:

For sample size between 15 and 30, the z- test procedure is used when the variable is far from being normally distributed or outlier is absent in the data.

Large Sample size:

For sample size 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

In the given exercise, we have provided a sample mean, sample size, and population standard. In each case, use the one-mean z-test to perform the required hypothesis test at the 5% significance level.

x鈥�=20,n=24,蟽=4,H0:渭=22,Ha:渭鈮�22

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

Cheese Consumption. Refer to Problem 24. The following table provides last year's cheese consumption: in pounds, 35 randomly selected Americans.

4629333842403433323628472642363245243928334433263727313637373622443629

  1. At the 10%significance level, do the data provide sufficient evidence to conclude that last year's mean cheese consumption for all Americans has increased over the 2010 mean? Assume that 蟽=6.9lb. Use a z-test. (Note: The sum of the data is 1218lb.)
  2. Given the conclusion in part (a), if an error has been made, what type must it be? Explain your answer.

In each of Exercises 9.41-9.46 ,determine the critical values for a one-mean z-test. For each exercise, draw a graph that illustrates your answer

A two-tailed test with伪=0.05

Job Gains and Losses. In the article "Business Employment Dynamics: New Data on Gross Job Gains and Losses" (Monthly Labor Review, Vol. 127, Issue 4, pp. 29-42), J. Spletzer et al. examined gross job gains and losses as a percentage of the average of previous and current employment figures. A simple random sample of 20 quarters provided the net percentage gains (losses are negative gains) for jobs as presented on the WeissStats site. Use the technology of your choice to do the following.

a. Decide whether, on average, the net percentage gain for jobs exceeds 0.2. Assume a population standard deviation of 0.42. Apply

which we provide on the WeissStats site. Use the technology of your choice to do the following.

a. Obtain a normal probability plot, boxplot, histogram, and stemand-leaf diagram of the data.

b. Based on your results from part (a), can you reasonably apply the one-mean z-test to the data? Explain your reasoning.

c. At the 1%significance level, do the data provide sufficient evidence to conclude that the mean body temperature of healthy humans differs from 98.6掳F? Assume that 蟽=0.63掳F.
See all solutions

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