Question

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

      Ho:μ=70.7Ho:μ=70.7
      Ha:μ≠70.7Ha:μ≠70.7

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=68n=68 with mean M=72.7M=72.7 and a standard deviation of SD=5.3SD=5.3.

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

Solution :

= 70.7

= 72.7

s = 5.3

n = 68

This is the two tailed test .

The null and alternative hypothesis is

H₀ :   = 70.7

H_a : 70.7

Test statistic = t

= ( - ) / s / n

= (72.7 - 70.7) / 5.3 / 68

= 3.112

p(t >3.112 ) = 1-P (t<3.112 ) = 0.0030

P-value = 0.0030