Question

. In a large corporation the mean entry level salary is $27,000 with a standard deviation of σ = 6,000. The entry level salaries for a random sample of 15 employees with only high school degrees is X ̅ = $24,100 . Do people with only high school degrees earn less than the rest of the company? Conduct a one-tailed hypothesis test with  = .05.

2a. The hypothesis test should be... (highlight one) (1 point) a) one-tailed (directional) b) two-tailed (non-directional) 2b. According to your answers above, conduct the hypothesis test. STEP 1: State your hypotheses in both words and symbols. Be sure to clearly label your null and research (alternative) hypotheses. (4 points)

In words:

In symbols:

STEP 2: Find the critical value. (2 points)

STEP 3: Compute the appropriate test-statistic. (4 points)

STEP 4: Evaluate the null hypothesis (based on your answers to the above steps). REJECT or FAIL TO REJECT (highlight one) (1 point) Which is the best conclusion, according to your decision in

STEP 4? (Highlight one) (1 point)

a. People with only high school degrees make the same amount of money as the rest of the population.

b. People with only high school degrees make significantly more money than the rest of the population.

c. People with only high school degrees make significantly less money than the rest of the population.

2c. IF your decision had been to reject the null, what is the probability that you made a Type I error in this problem? (1 point

Answer 1

Let denote the entry-level salary of those with only a high school degree and mean entry-level salary with a standard deviation of σ. We are given,

= $ 27,000 (Hypothesized mean), σ = 6000 (Pop. Std. Dev), = $ 24,100 (Sample mean)

1. We are asked to test:

Vs at 5% level of significance.

H₀:  People with only high school degrees does not earn less than the rest of the company Vs H_a: People with only high school degrees earn less than the rest of the company

The appropriate statistical test to test the above (left tailed) one-tailed ( --'<' in the alternative ) hypothesis would be a One sample Z test for mean since the population standard deviation is known.

But before running this test, we must ensure that the data satisfies the assumptions of this test:

- The data is continuous - The observations are from a simple random sample - The data is normally distributed - The population standard deviation is known  

Assuming that all the assumptions are satisfied:

The test statistic is given by:

with critical region given by: for left - tailed test.

From standard normal table, looking for the area alpha = 0.05:

b. Critical value Z_0.05 = - 1.645

We may reject H0  if the test statistic falls in the critical region Z <  -1.645

c. From the given data,

Substituting the values obtained in the test statistic:

= -1.87

Comparing the test statistic with the critical value, since, Z = -1.87 < - 1.645 lies in the rejection region, we may reject H0 at 5% level.

We may conclude that the data provides sufficient evidence to support the claim that people with only high school degrees earn less than the rest of the company.

4.  People with only high school degrees make significantly less money than the rest of the population.

5. The type I error is the probability of rejecting a true null hypothesis which can be obtained by looking for the critical area corresponding to the Z statistic in the standard normal curve:

We get Type I error = 0.03074