In: Statistics and Probability
In a survey to determine whether the daily caloric
intake of the adolescent girls in
Ahafo-Ano South district of Ashanti is less than 2000 kcal, a
sample of 500 adolescent
girls were randomly sampled for the study. The mean daily caloric
intake from this
sample was 1985 kcal, with a standard deviation of 210 kcal. Let α
= 0.05. Assume
you do not know the population variance; can the researchers
conclude that the
population mean is less than 2000 kcal
please show all workings step by step using the 9 steps in hypothesis testing!
Solution :
Given that,
= 2000
= 1985
= 210
n = 500
The null and alternative hypothesis is ,
H0 : = 2000
Ha : < 2000
This is the left tailed test .
= 0.05
Z =
Z0.05 = -1.645
The Critical value is -1.645
Test statistic = z
= ( - ) / / n
= (1985 - 2000) / 210 / 500
= -1.60
Test statistic = -1.60
P-value = P (Z < -1.60) = 0.0548
P-value = 0.0548
= 0.05
0.0548 > 0.05
P-value >
Fail to reject the null hypothesis .
There is not sufficient evidence to claim the test.