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mihalych1998 [28]
3 years ago
7

A survey claims that a college graduate from Smith College can expect an average starting salary of $ 42,000. Fifteen Smith Coll

ege graduates had an average starting salary of $ 40,800 with a standard deviation of $ 2250. At the 1 % level of significance, can we conclude that the average starting salary of the graduates is significantly less that $42,000?
Mathematics
1 answer:
jek_recluse [69]3 years ago
3 0
<h2>Answer with explanation:</h2>

Let \mu be the average starting salary ( in dollars).

As per given , we have

H_0: \mu=42000\\\\ H_a:\mu

Since H_a is left-tailed , so our test is a left-tailed test.

WE assume that the starting salary follows normal distribution .

Since population standard deviation is unknown and sample size is small so we use t-test.

Test statistic : t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}} , where n= sample size , \overline{x} = sample mean , s = sample standard deviation.

Here , n= 15 , \overline{x}=  40,800  , s= 225

Then, t=\dfrac{40800-42000}{\dfrac{2250}{\sqrt{15}}}\approx-2.07

Degree of freedom = n-1=14

The critical t-value for significance level α  = 0.01 and degree of freedom 14 is 2.62.

Decision : Since the absolute calculated t-value (2.07) is less than the  critical t-value., so we cannot reject the null hypothesis.

Conclusion : We do not have sufficient evidence at 1 % level of significance to support the claim that  the average starting salary of the graduates is significantly less that $42,000.

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