Question

You wish to test the following claim (HaHa) at a significance level of α=0.05α=0.05.

      Ho:μ=83.8Ho:μ=83.8
      Ha:μ≠83.8Ha:μ≠83.8

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=75n=75 with mean ¯x=78.4x¯=78.4 and a standard deviation of s=13.4s=13.4.

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 not equal to 83.8.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 83.8.
• The sample data support the claim that the population mean is not equal to 83.8.
• There is not sufficient sample evidence to support the claim that the population mean is not equal to 83.8.

Answer 1

Solution :

= 83.8

=78.4

S =13.4

n = 75

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :    = 83.8

H_a :     83.8

Test statistic = t

= ( - ) / S / n

= (78.4-83.8) / 13.4 / 75

= −3.49

Test statistic = t = −3.49

P-value =0.0008

= 0.05  

P-value <

0.0008 < 0.05

Reject the null hypothesis .

There is sufficient evidence to claim that the population mean μ is different than 83.8, at the 0.05 significance level.