Question

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 $98.6°\mathrm{F}$? Assume that $\sigma =0.63°\mathrm{F}$.

Short answer

A hypothesis expresses your expectations for the results of your investigation. It's a hypothesis for your study topic that hasn't been tested yet. You may need to construct many hypotheses to cover different parts of your research issue for certain research initiatives.

Step-by-step solution

Introduction

• The first step is for the analyst to state the two hypotheses so that only one can be right.
• The next step is to formulate an analysis plan, which outlines how the data will be evaluated.
• The third step is to carry out the plan and physically analyze the sample data.
• The fourth and final step is to analyze the results and either reject the null hypothesis, or state that the null hypothesis is plausible, given the data.

a)

Given information:

The random sample of 20 quarters provided the net percentage gain for job as presented on Weiss Stats site.

Calculation:

Write the null and alternative hypothesis.

Null hypothesis.

$H_0:\mu =0.5$

The data does not provide sufficient evidence that on average the net percentage gain for jobs exceeds $0.5$.

Alternative hypothesis

$H_0:\mu >0.2$

The data provide sufficient evidence that on average the net percentage gain for jobs exceeds $0.5.$

The significance level is $\alpha =0.05$

Step 3:Calculate the value of the test statistic 

Calculate the value of the test statistic and P-value by using MINITAB.

MINITAB output

One sample Z: Gain

Test of mu$=0.2\mathrm{vs}>0.2$

The assumed standard deviation$=0.42$

From the MINITAB output, the value of test statistic is $1.01$ and the P-value is 0.156.

If $P\le \alpha$, then reject the null hypothesis.

Here, the P-value is 0.156 which is greater than the level of significance.

$P(=0.156)>\alpha (=0.05)$

The null hypothesis is not rejected at $5\%$level.

Thus, the data does not provide sufficient evidence to conclude that on average the net percentage gain for job exceeds 0.5.

b. Sketch the various graph for the given problem

The random sample of 20 quarters provided the net percentage gain for job as presented on Weiss Stats site.

Calculation:

Construct the normal probability plot by using MINITAB.

MINITAB output:

From the probability plot, the observations are closer to straight line with one outlier.