Question

consider the following hypothesis ho: u=470 ha: u does not equal 470

The population is normaly distributed with a population standard deviation of 53

a-1 calculate the value of the test statistic with x= 492 and n=90

a-2 what is the conclusion at 10% significance level

a-3 interpret the results at a=.1

b-1 calculate the value of the test statistic at x= 438 and n=90

b-2 what is the conclusion at 5% significance level

b-3 interpret the results at a= .05

Answer 1

a1)
Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (492 - 470)/(53/sqrt(90))
z = 3.94

a2)

P-value Approach
P-value = 0.0001
As P-value < 0.1, reject the null hypothesis.

a3)

There is sufficient evidence to conclude that mean is different from 470

b1)

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (438 - 470)/(53/sqrt(90))
z = -5.73

b2)

P-value Approach
P-value = 0
As P-value < 0.05, reject the null hypothesis.

b3)

There is sufficient evidence to conclude that mean is different from 470