Question

2. Assu me that a simple random sample has been selected from a normally distributed population and e given claim. Identify the claim, the null and alternative hypotheses, test statistic, critical test th value(s), P-valu claim. Draw the bell-curve and identify: the critical value(s), the critical region(s) by shading, and the e and compare to alpha, and state the final conclusion that addresses the original test statistic. A large software company gives job applicants a test of programming ability and the mean for that test has been 175 in the past. Twenty-eight job applicants are randomly selected from one large human resources company and they produce a mean score of 182 and a standard deviation of 15. Use a 0.05 level of significance to test the claim that this sample comes from a population with a mean score greater than 175.

Answer 1

Answer:

Single sample t test

This is upper tail test

Claim is alternate hypothesis.

The sample come from a population with mean score greater than 175.

$t = \frac { (\bar x - \mu)} {\frac {s} {\sqrt{n}}}$

$t = \frac{(182-175)}{\frac{15}{\sqrt{28}}}$

=2.4694               

Table value of t with 27 DF at 0.05 level =1.7033

Rejection Region: Reject Ho if t > 1.7033

Calculated t =2.4694   falls in the rejection region

The null hypothesis is rejected.

P value = 0.0101 which is < 0.05 level. Ho is rejected.

There is enough evidence to support the claim.

t Test for Hypothesis of the Mean
Data
Null Hypothesis                m=	175
Level of Significance	0.05
Sample Size	28
Sample Mean	182
Sample Standard Deviation	15
Intermediate Calculations
Standard Error of the Mean	2.8347
Degrees of Freedom	27
t Test Statistic	2.4694
Upper-Tail Test
Upper Critical Value	1.7033
p-Value	0.0101
Reject the null hypothesis