The market firm salary.com reported that the mean annual earnings of all family practitioners in the US was $178,258. A random sample of 55 family practitioners in LA that month had mean earnings of mean=$192,340 with a standard deviation of $42,387. Does the data provide sufficient evidence to conclude that the mean salary for family practitioners is LA is greater than the national average? A. state the null and alternate hypothesisB. compute the value of the t statistic. C. State your conclusion using 0.05 level of significance.

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Asked Jul 22, 2019
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The market firm salary.com reported that the mean annual earnings of all family practitioners in the US was $178,258. A random sample of 55 family practitioners in LA that month had mean earnings of mean=$192,340 with a standard deviation of $42,387. Does the data provide sufficient evidence to conclude that the mean salary for family practitioners is LA is greater than the national average? 

A. state the null and alternate hypothesis

B. compute the value of the t statistic. 

C. State your conclusion using 0.05 level of significance. 

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Expert Answer

Step 1

A. Hypotheses:

Denote µ as the population mean salary for family practitioners in LA. The claim is that mean salary of for family practitioners in LA is greater than the national average. The hypotheses that is appropriate to this claim are as follows:

Null hypothesis:

H0: µ = 178,258

That is, the mean salary of for family practitioners in LA is same as the national average.

Alternate hypothesis:

H1: µ > 178,258

That is, the mean salary of for family practitioners in LA is greater than the national average.

Step 2

B. Compute the values of the test statistics.

The formula for test statistic is,

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о х — Но t calc n

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Step 3

Where x-bar is the sample means, µ0 hypothesized mean, s is the sample standard deviation and n is sample size, respectively.

Substitute x-bar = 192,340...

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192,340-178,258 tcalc 42,387 55 14,082 5,715.46 = 2.46

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