Question

In: Statistics and Probability

In a survey to determine whether the daily caloric intake of the adolescent girls in Ahafo-Ano...

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!

Solutions

Expert Solution

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.


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