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Chapter 9: Q. 9.81 (page 380)

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

x¯=23,n=24,σ=4,H0:μ=22,Ha:μ≠22

Short Answer

Expert verified

The value of z is 1.22, critical value is±1.96,P=0.221and do not rejectH0.

Step by step solution

01

Step 1. Given information.

Consider the given question,

x¯=23,n=24,σ=4,H0:μ=22,Ha:μ≠22

02

Step 2. Consider the test hypothesis.

Consider the given hypothesis,

μis the population mean.

The test hypothesis,

H0:μ=22vsHa:μ≠22

Therefore, this is two tailed test.

And the level of significance is α=0.05.

We want to find the hypothesis test about the mean μ,

z=x¯-μ0σn=23-22424=1.22

Therefore, this is left tailed test withα=0.05.

03

Step 3. Take the critical values.

The critical values are given below,

±za2=±z0.052=±z0.025=±1.96

The rejection region is z<-za2or z>za2, i.e., z<-1.96or z>1.96.

Here, z=1.22>-z0.025=-1.96

and z=1.22<1.96

Hence, we do not reject H0at 5% level of significance as the value ofz does not fall in the reject region.

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Most popular questions from this chapter

In the article "Business Employment Dynamics: New data on Gross Job Gains and Losses", 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 20quarters provided the net percentage gains for jobs as presented on the WeissStats site. Use the technology of your choice to do the following.

Part (a): Decide whether, on average, the net percentage gain for jobs exceeds 0.2. Assume a population standard deviation of 0.42. Apply the one-mean z-test with a 5%significance level.

Part (b): Obtain a normal probability plot, boxplot, histogram and stem-and-leaf diagram of the data.

Part (c): Remove the outliers from the data and then repeat part (a).

Part (d): Comment on the advisability of using thez-test here.

9.89 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 the one-mean z-test with a 5% significance level.
b. Obtain a normal probability plot, boxplot, histogram, and stem-and-leaf diagram of the data.
c. Remove the outliers (if any) from the data and then repeat part (a).
d. Comment on the advisability of using the z-test here.

9.128 Two-Tailed Hypothesis Tests and CIs. 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 α, the null hypothesis H0:μ=μ0will be rejected in favor of the alternative hypothesis H2:μ>μ0if and only if μ0lies outside the (1-α)-level confidence interval for μ. In each case, illustrate the preceding relationship by obtaining the appropriate one-mean t-interval (Procedure 8.2 on page 338 ) and comparing the result to the conclusion of the hypothesis test in the specified exercise.
a. Exercise 9.113
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 σ=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.

Fair Market Rent. According to the document Out of Reach published by the National Low Income Housing Coalition, the fai market rent (FMR) for a two-bedroom unit in the United States is 949 A sample of 100 randomly selected two-bedroom units yielded the data on monthly rents, in dollars, given on the WeissStats site. Use the technology of your choice to do the following.

a. At the 5 % significance level, do the data provide sufficient evidence to conclude that the mean monthly rent for two-bedroom units is greater than the FMR of $949? Apply the one-mean t-test.

b. Remove the outlier from the data and repeat the hypothesis test in part (a).

c. Comment on the effect that removing the outlier has on the hypothesis test.

d. State your conclusion regarding the hypothesis test and explain your answer.
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