Question

(1 point) A random sample of 100100 observations from a population with standard deviation 13.8313.83 yielded a sample mean of 92.392.3.

1. Given that the null hypothesis is μ=90μ=90 and the alternative hypothesis is μ>90μ>90 using α=.05α=.05, find the following:
(a) Test statistic ==  
(b) P - value:  
(c) The conclusion for this test is:

A. Reject the null hypothesis
B. There is insufficient evidence to reject the null hypothesis
C. None of the above

2. Given that the null hypothesis is μ=90μ=90 and the alternative hypothesis is μ≠90μ≠90 using α=.05α=.05, find the following:
(a) Test statistic ==  
(b) P - value:  
(c) The conclusion for this test is:

A. Reject the null hypothesis
B. There is insufficient evidence to reject the null hypothesis
C. None of the above

Answer 1

1)

H0: = 90 , Ha: > 90

a)

Test statistics

z = - / / sqrt(n)

= 92.3 - 90 / 13.83 / sqrt(100)

= 1.66

b)

p-value = P (Z > z)

= P (Z > 1.66)

= 0.0485

c)

Since p-value < 0.05 level, we have sufficient evidence to reject H0.

Reject the null hypothesis.

2)

H0: = 90 , Ha: 90

a)

Test statistics

z = - / / sqrt(n)

= 92.3 - 90 / 13.83 / sqrt(100)

= 1.66

b)

p-value = 2 * P (Z > z)

=2 * P (Z > 1.66)

= 0.097

c)

Since p-value > 0.05 level we do not have sufficient evidence to reject H0>

There is insufficient evidence to reject null hypothesis

Test statistics

z = - / / sqrt(n)

= 92.3 - 90 / 13.83 / sqrt(100)

= 1.66

b)

p-value = P (Z > z)

= P (Z > 1.66)

= 0.0485