Question

You wish to test the following claim (HaHa) at a significance level of α=0.001α=0.001.

      Ho:μ=57.1Ho:μ=57.1
      Ha:μ<57.1Ha:μ<57.1

You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:

data

64.2

53.3

64.2

38.6

54.4

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:

Ho:μ = 57.1 vs Ha:μ < 57.1

Sample size = n = 5

64.2,53.3,64.2,38.6,54.4

a)

To find the test statistic , we need to find the sample mean and sample standard deviation.

Using calculator ,

sample mean = = 54.94

sample SD = s = 10.505617544914

The test statistic t is

t =   = [54.94 - 57.1]/[10.505617544914 /5] = -0.460

Test statistic : -0.460

b)

d.f = n - 1 = 5 - 1 = 4

< sign in Ha indicates that the test is One tailed Left sided

t = -0.460

Using calculator ,

p value = 0.3347