Question

A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.4. The population standard deviation is assumed to equal 0.40.

a. Construct the hypotheses H0 and HA

b. What is the p-value if a =0.05?

c. At the 5% significance level, does the university reject the null hypothesis?

Answer 1

Given : µ = 3.50 , σ = 0.40, n=36 , $1588094221335_blob.png$ = 3.40 , α = 0.05

#a)

Step 1) Establish the hypothesis.

A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50.

H0 : µ = 3.50               Vs   H1 : µ > 3.50

Step 2) calculating test statistics.

As sample size is greater than 30, We use z statistic

Z = ​​​​ $1588094221233_blob.png$     =       = -1.5

3.40-3.50 0.40/36

#b)

Step 3) P value

As α = 0.05 and right tail test.

From standard normal table P(Z > -1.5) = 1- P(Z < -1.5)   = 1- 0.0668 = 0.9332

For z = -1.5   , P value = 0.9332

(a) Table of Areas to the Left of z Z .00 .01 .02 .03 -3.4 .0003 .0003 .0003 .0003 -3.3.0005 00050005.0004 -3.2 .0007.0007.0006.0006 -3.1 .0010 .0009.0009.0009 -3.0 .0013 .0013 .0013 .0012 -2.9 .0019 .0018 .0018 .0017 -2.8 .0026 .0025 .0024 .0023 -2.7 .0035 .0034 .0033 0032 -2.6.0047.0045.0044.0043 -2.5 .0062 .0060.0059.0057 -2.4 .0082.0080.0078 .0075 -2.3 .0107 0104 .0102 .0099 -2.2 .0139 0136 .0132 0129 -2.1 .0179 .0174 .0170 .0166 -2.0.0228 0222 0217 0212 -1.9 .0287 0281 0274 0268 -1.8 .0359 .0351.0344 0336 -1.7 .0446 .0436 .0427 .0418 -1.6 .0548.0537 .0526 .0516 -1.5.0668.0655 .0643.0630 -1.4 .0808 0793 0778 .0764

#c)

Step 4) Decision rule:

Since ,P value is 0.9332 > 0.05 ( Level of significance ), we do not reject H0

Step 5) Conclusion: There is not sufficient evidence to reject   H0 . At the 5% significance level, the university do not reject the null hypothesis.