Question

A simple random sample generated 12 male and 18 female adults identified by their primary care physicians as being over-weight. These adults were fed a special high protein diet for a month and had a sample mean weight loss of 10 pounds with a sample standard deviation of 3.2 pounds. We would like to conduct a test to determine whether the average weight loss for all adults is less than 11 pounds at a 1% level of significance.

What is the appropriate hypothesis for this test?

a. Ho: μ ≠ 11 vs Ha: μ = 11  

b.
H₀: x̄ = 11 vs. Ha: x̄ ≠ 11

c. Ho: μ = 11 vs Ha: μ ≠ 11  

d. Ho: μ = 11 vs Ha: μ < 11

e. Ho: μ < 11 vs Ha: μ = 11

Answer 1

Solution :

Given that,

=10 pounds

s = 3.2 pounds

n = 30

a.) Hypothesis:

H0 : μ = 11

Ha : μ < 11

Test Statistic:

t = ( - μ) / (s /n)

t = (10 - 11 ) / ( 3.2 / 30 )

t = -1.712

P - value = 0.0488

if P- value < 0.05 then reject H0.

P-value > 0.05, we Fail to reject H0.

The average weight loss for all adults is not less than 11 pounds.