Question

A large software company gives job applicants a test of programming ability and the mean for that test has been 182 in the past. Twenty five job applicants are randomly selected, and they produce a sample mean score of 186 and a sample standard deviation of 12. Use a 5% level of significance to test the claim that this sample comes from a population with a mean score greater than 182. Assume the distribution is normally distributed.(Round to two decimal places)

(a) Critical Values:

(b) Construct a 95% confidence interval for the mean score. (Round to 2 decimal places)  

Answer 1

a) hare population standard deviation is unknown so we use t distribution for finding critical values. .given significance level 0.05 and right tailed hypothesis (because we want to test whether mean is greater than 182 or not) and degrees of freedom 25 - 1=24 , we get critical value

t=

b)

CI [181.05, 190.95]

values above 182 lies in this confidence interval. Hence mean can be greater than 182. cliam is correct

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