Question

# Ten people went on a diet for a month. The weight losses experienced​ (in pounds) are...

Ten people went on a diet for a month. The weight losses experienced​ (in pounds) are given below. The negative weight loss is a weight gain. Test the hypothesis that the mean weight loss was more than 0​, using a significance level of 0.05. Assume the population distribution is Normal. 3​, 7​, 10​, 0​, 3​, 7​, 5​, 5​, 1​, and negative 3

 Values ( X ) 3 0.64 7 10.24 10 38.44 0 14.44 3 0.64 7 10.24 5 1.44 5 1.44 1 7.84 -3 46.24 Total 38 131.6

Mean

Standard deviation

To Test :-

H0 :-

H1 :-

Test Statistic :-

t = 3.1425

Test Criteria :-
Reject null hypothesis if

Result :- Reject null hypothesis

Decision based on P value
P - value = P ( t > 3.1425 ) = 0.0059
Reject null hypothesis if P value <    level of significance
P - value = 0.0059 < 0.05 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

There is sufficient evidence to support the claim that the mean weight loss was more than 0​ at 5% significance level.

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