Question

 

1) Test the claim that the mean GPA of night students is smaller than 3.1 at the 0.05 significance level.

The null and alternative hypothesis would be:

H0:μ=3.1H0:μ=3.1
H1:μ≠3.1H1:μ≠3.1

H0:p≥0.775H0:p≥0.775
H1:p<0.775H1:p<0.775

H0:p≤0.775H0:p≤0.775
H1:p>0.775H1:p>0.775

H0:μ≤3.1H0:μ≤3.1
H1:μ>3.1H1:μ>3.1

H0:p=0.775H0:p=0.775
H1:p≠0.775H1:p≠0.775

H0:μ≥3.1H0:μ≥3.1
H1:μ<3.1H1:μ<3.1

The test is:

right-tailed

two-tailed

left-tailedBased on a sample of 65 people, the sample mean GPA was 3.05 with a standard deviation of 0.05
The p-value is:  (to 2 decimals) ______

Based on this we:

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

2) You wish to test the following claim (HaHa) at a significance level of α=0.001α=0.001.

      Ho:μ=52.8Ho:μ=52.8
      Ha:μ>52.8Ha:μ>52.8

You believe the population is normally distributed and you know the standard deviation is σ=6.5σ=6.5. You obtain a sample mean of M=53.5M=53.5 for a sample of size n=72n=72.

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

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

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 greater than 52.8.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 52.8.
• The sample data support the claim that the population mean is greater than 52.8.
• There is not sufficient sample evidence to support the claim that the population mean is greater than 52.8.

Answer 1

Solution ;-

Given that ,

= 3.1

= 3.05

= 0.05

n = 65

This is the left tailed test .

The null and alternative hypothesis is ,

H0 :   = 3.1

H1 : < 3.1

Test statistic = z

= ( - ) / / n

= ( 3.1 - 3.05 ) / 0.05 / 65

= 8.06

The test statistic = 8.06

P - value = P ( Z < 8.06 ) = 1.00

P-value = 1.00

= 0.05  

1.00 > 0.05

P-value >  

Fail to reject the null hypothesis

( 2 )

Given that ;

M = 52.8

= 53.5

= 6.5

n = 72

This is the right tailed test .

The null and alternative hypothesis is ,

H0 :   = 52.8

Ha : > 52.8

Test statistic = z

= (M - ) / / n

= ( 53.5 - 52.8 ) / 6.5 / 72

= 0.914

The test statistic = 0.914

P - value = P( Z > 0.914 )

= 1 - P ( Z < 0.914 )

= 1 - 0.8196

= 0.1804

P-value = 0.1804

= 0.001

0.1804 > 0.001

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 52.8.