Question

The Dean of ASBE School of Business is concerned that grades in the MBA program are distributed appropriately. Too many high grades or too many low grades would pose a problem. We wish to test the claim that the mean GPA of ASBE students is smaller than 3.3 at the .005 significance level.

The null and alternative hypothesis would be:

• H0:p=3.34H0:p=3.34
  Ha:p>3.34Ha:p>3.34
• H0:μ=3.3H0:μ=3.3
  Ha:μ≠3.3Ha:μ≠3.3
• H0:p=3.34H0:p=3.34
  Ha:p<3.34Ha:p<3.34
• H0:μ=3.3H0:μ=3.3
  Ha:μ<3.3Ha:μ<3.3
• H0:p=3.34H0:p=3.34
  Ha:p≠3.34Ha:p≠3.34
• H0:μ=3.3H0:μ=3.3
  Ha:μ>3.3Ha:μ>3.3

The test is:

left-tailed

two-tailed

right-tailed

Based on a sample of 75 student grades, the sample mean GPA was 3.28 with a standard deviation of 0.02

The test statistic is:  (Round to 3 decimals)

Based on this we:

• Fail to reject the null hypothesis
• Reject the null hypothesis

A shareholders' group is lodging a protest against your company. The shareholders group claimed that the mean tenure for a chief exective office (CEO) was at least 9 years. A survey of 59 companies reported in The Wall Street Journal found a sample mean tenure of 7.3 years for CEOs with a standard deviation of s=s= 5 years (The Wall Street Journal, January 2, 2007). You don't know the population standard deviation but can assume it is normally distributed.

You want to formulate and test a hypothesis that can be used to challenge the validity of the claim made by the group, at a significance level of α=0.01α=0.01. Your hypotheses are:

      Ho:μ=9Ho:μ=9
      Ha:μ<9Ha:μ<9

What is the test statistic for this sample?
test statistic =  (Report answer accurate to 3 decimal places.)

What is the p-value for this sample?
p-value =  (Report answer accurate to 4 decimal places.)  

The p-value is...

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the population mean is less than 9.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 9.
• The sample data support the claim that the population mean is less than 9.
• There is not sufficient sample evidence to support the claim that the population mean is less than 9.

Answer 1

Given:

Claim : Ghe mean GPA of ASBE students is smaller than 3.3 at significance level 0.005

The null and alternative hypotheses is

Ho : μ = 3.3

Ha : μ < 3.3

Since alternative hypothesis contain < sign,

The test is left-tailed test

Sample size, n = 75

Sample mean, = 3.28

Standard deviation, s = 0.02

Test statistics :

t = - μ/s/√n

= 3.28 - 3.3/0.02/√75

= -8.660

Test statistics is t = -8.660

Degree of freedom, df = n-1 = 75-1 = 74

At 0.005 the critical value of a t with degree of freedom, df = 74 is -2.644

Rejection rule:

Reject Ho if to < -2.644

Since to < -2.644 , = 0.005 we reject null hypothesis.

Decision: Reject null hypothesis.

Conclusion : There is sufficient evidence to conclude that the mean GPA of ASBE students is smaller than 3.3 at the .005 significance level.

2) Given:

The null and alternative hypothesis is

Ho : μ = 9

Ha : μ < 9

Sample size, n = 59

Sample mean, = 7.3

Standard deviation, s= 5

Test statistics is

t = - μ/s/√n

= 7.3 - 9/5/√59

= -2.612

Test statistics is t = -2.612

Degree of freedom, df = n-1 = 59-1 = 58

At 0.01 significance level the critical value of t with degree of freedom, df = 58 is -2.392

Rejection rule:

Reject Ho if to < -2.392

Since to < -2.392 , we reject null hypothesis.

Decision: Reject null hypothesis.

Conclusion:

• There is sufficient evidence to warrant rejection of the claim that the population mean is less than 9.