Question

# A magazine publishes the top 100 companies to work for every​ year, which includes the percentage...

A magazine publishes the top 100 companies to work for every​ year, which includes the percentage growth in jobs at each company. The output to the right shows the regression of the 2012 job growth​ (%) on the 2010 job growth. Use the output to the right to complete parts​ a) through​ d).

Dependent variable​ is: Job Growth 2012 ​

R-squaredequals22.9​%

s=9.974 with 28-2=26 degrees of freedom

Variable Coefficient SE(Coeff) t-Ratio P-Value

Intercept 2.507 1.437 1.74 0.0937

Job Growth 0.312 0.258 1.21 0.2372 ​

2010

a) State the hypotheses about the slope​ (both numerically and in​ words).

Upper H 0​: The job growth in 2012 is not or is related to the job growth in​ 2010: beta1 ▼ not equals or equals 0.

Upper H Subscript Upper A​: The job growth in 2012 ▼ is not or is related to the job growth in​ 2010: beta1 ▼ not equals or equals 0. ​

b) Assuming that the assumptions for inference are​ satisfied, perform the hypothesis test and state your conclusion in context. Assume alphaequals0.05.

Identify the test statistic.

The test statistic is (____) ​(Do not​ round.)

Identify the​ P-value.

​P-value=(____)​(Do not​ round.)

The ▼ low or high ​P-value indicates there ▼ is insufficient or is sufficient evidence of a linear relationship between the job growth values. ​

c) Explain what the​ R-squared in this regression means. Choose the correct answer below.

A. ​Overall, the job growth in 2010 is 22.9​% of the job growth in 2012.

B. 22.9​% of the variation in the job growth in 2012 is accounted for by the job growth in 2010.

C. 22.9​% of the variation in the job growth in 2010 is accounted for by the job growth in 2012.

D. ​Overall, the job growth in 2012 is 22.9​% of the job growth in 2010.

​d) Do these results indicate​ that, in​ general, companies with a higher job growth in 2010 had a higher job growth in​ 2012? Explain.

A. ​Yes, because there is significant evidence of a linear relationship with a negative slope.

B. Yes​, because there is significant evidence of a linear relationshipnbsp with a positive slope.

C. No​, because there is insufficient evidence of a linear relationship.

D. ​No, because there is insufficient evidence of a linear​ relationship, but the slope is negative. .

a)

The hypotheses are:

H0: The job growth in 2012 is not related to the job growth in​ 2010.

Ha: The job growth in 2012 is related to the job growth in​ 2010.

In symbols:

b)

The test statistic is

t = 0.258

The p-value is: 0.2372

Since p-value is greater than 0.05 so we fail to reject the null hypothesis.

The high ​P-value indicates there is insufficient evidence of a linear relationship between the job growth values. ​

c)

B. 22.9​% of the variation in the job growth in 2012 is accounted for by the job growth in 2010.

d)

C. No​, because there is insufficient evidence of a linear relationship.

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