Question

You wish to test the following claim (Ha) at a significance level of α=0.02

      Ho:μ=55.5
      Ha:μ>55.5

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=24 with a mean M=59.6 and a standard deviation of SD=10.1

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

The p-value is...

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

This p-value leads to a decision to...

• (A)reject the null
• (B)accept the null
• (C)fail to reject the null

As such, the final conclusion is that...

• (A)There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 55.5.
• (B)There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 55.5.
• (C)The sample data support the claim that the population mean is greater than 55.5.
• (D)There is not sufficient sample evidence to support the claim that the population mean is greater than 55.5.

Answer 1

Solution :

This is the right tailed test,  

The null and alternative hypothesis is ,

H₀ :   = 55.5

H_a : > 55.5

Test statistic = t =

= ( - ) / s / n

= (59.6 - 55.5) / 10.1 / 24

Test statistic = t = 1.989

degrees of freedom = n - 1 = 24 - 1 = 23

P(t > 1.989) = 1-P (t < 1.989) = 1 - 0.9706

P-value = 0.0294

= 0.02

B) The p-value is greater than α

C) This p-value leads to a decision to fail to reject the null

B)There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 55.5.