Question

1. A Zone diet is one with a 40%-30%-30% distribution of carbohydrate, protein, and fat, respectively, and is based on the book Enter the Zone. In a study conducted by researchers Christopher Gardner and associates, 79 subjects were administered the Zone diet. After 12 months, the mean weight loss was 6 kg, with a standard deviation of 5.4 kg. Do these results suggest that the weight loss was statistically significantly greater than zero at the 0.05 level of significance? Use the p-value method of hypothesis testing. What do you think about the results? Do you feel the diet is effective for weight loss?

Questions:

1, Requirements?

2, Hypothesis Test?

3,Do you think the diet is effective for weight lost?

4, what do you think about the results?

Answer 1

Given that,
population mean(u)=0
sample mean, x =6
standard deviation, s =5.4
number (n)=79
null, Ho: μ=0
alternate, H1: μ>0
level of significance, α = 0.05
from standard normal table,right tailed t α/2 =1.665
since our test is right-tailed
reject Ho, if to > 1.665
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =6-0/(5.4/sqrt(79))
to =9.876
| to | =9.876
critical value
the value of |t α| with n-1 = 78 d.f is 1.665
we got |to| =9.876 & | t α | =1.665
make decision
hence value of | to | > | t α| and here we reject Ho
p-value :right tail - Ha : ( p > 9.8758 ) = 0
hence value of p0.05 > 0,here we reject Ho
ANSWERS
---------------
1.
null, Ho: μ=0
alternate, H1: μ>0
2.
t test for single mean with unknown population standard deviation
3.
test statistic: 9.876
critical value: 1.665
decision: reject Ho
p-value: 0
we have enough evidence to support the claim that the weight loss was statistically significantly greater than zero
4.
yes,
i feel the diet is effective for weight loss.