Write the word or phrase that best completes each statement to answer the questi

Question

Write the word or phrase that best completes each statement to answer the question. Assume that a simple random sample has been selected from a normally distributed population and test the give claim. Identify the null and alternative hypotheses, test statistic, critical value(s) or P-value (or range of P-value) as appropriate, and state the final conclusion that addresses the original claim. A large software company gives job applicants a test of programming ability and the mean for that test been 160 in the past. Twenty-five job applicants are randomly selected from one large university and they produce a mean score and standard deviation of 183 and 12, respectively. Use a 0.05 level of significance to test the claim that this sample comes from a population with a mean score greater than 160. Use the P-value method of testing hypotheses

Explanation / Answer

Mean for the test =160

25 job applicants are randomly selected

Mean of 25 Job applicant=183

S.D. of 25 Job applicant= 12

At 5% level to test the claim that this sample comes from a population with mean greater than 160

H0: u=160 ; Null hypothesis

H1: u>160; alternate hypothesis

Test statistics:

X-u/[s.d./sqrt(n)] ~ Normal distribution

Under H0

T.S.= (183-160)/[12/Sqrt(25)]=(23*5)/12=9.58333

P(Z>9.58333)=0

Method 1:

We are carrying out a 5% one tailed test. The probability we have obtained is less than 5%, so we have sufficient evidence to reject H0 at the 5% level.

Therefore it is reasonable to conclude that this sample comes from a population with a mean score is greater than 160.

Method 2: From the Tables, P(Z >1.6449) = 0.05, so 1.6449 is the critical value for a one tailed 5% test. The test statistic of 9.5833 exceeds this critical value, so we reach the same conclusion as we did for Method 1.

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