Question

you wish to test the following claim ( H a ) at a significance level of α = 0.10 .

H o : μ = 68.9 H a : μ ≠ 68.9

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 16 with mean M = 56.1 and a standard deviation of S D = 12.8 .

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) α or greater than α

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

reject the null or accept the null or 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 not equal to 68.9.

b) There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 68.9.

c) The sample data support the claim that the population mean is not equal to 68.9.

d) There is not sufficient sample evidence to support the claim that the population mean is not equal to 68.9.

Answer 1

population men (mu) = 68.9

sample mean xbar = 56.1

sample size n = 16

standard deviation = 12.8

null hypothesis Ho;=68.9

alternative hypothesis Ha;68.9

using t -test statistic formula

t= (-) / (s/)

putting the values in the formula

t=(56.1-68.9) / (12.8/)

t=(56.1-68.9) / (3.2)

t=(-12.8) / (3.2)

t= -4

degree of freedom=n-1

=16-1

=15

alpha value=0.10

using degree of freedom 15 and alpha value 0.10 in t -value table to find p value

p value =0.0012

= 0.0012 < 0.10

p value is less than significance level, rejecting the null hypothesis

Conclusion:- since p value is less than significance level,result is significant and we have rejected the null hypothesis

So, we have insufficient evidence to warrant the rejection of claim

option (b)