Question

You wish to test the following claim (Ha) at a significance level of α=0.002.

      Ho:μ=79.8
      Ha:μ<79.8

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=30 with mean M=67.4 and a standard deviation of SD=16.5.

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 =

Answer 1

n=30,  = 79.8

= 67.4 , s = 16.5

= 0.002

null and alternative hypothesis is

Ho:   = 79.8

Ha:   < 79.8

formula for test statistics is

t = -4.116218

test statistics (t) = -4.116

now calculate P-Value for this one tailed test with df= n-1 = 30- =29, using following

excel command we get p-value as,

P-Value = 0.0001

decision rule is,

Reject Ho if (P-Value) < ( )

Here, ( P-Value = 0.0001) < ( = 0.002 )

Hence,

Null hypothesis is rejected.