When 40 people used the Atkins diet for one year their mean

When 40 people used the Atkins diet for one year, their mean weight was -2.1 lbs (the negative number here indicating loss). Assume that the standard deviation of all such weight changes is 4.8 lbs and use a 0.05 significance level to test the claim that the mean weight change is less than zero.

What is(are) the critical value(s)?

Solution

Let n be number of people used the Atkins diet for one year = 40

mean weight (Xbar) = -2.1 (negative number indicates that loss)

standard deviation (sd) = 4.8

level of significance (alpha) = 0.05

We have to test the claim that,

H0 : mu = 0 Vs H1 : mu < 0

The test is one sided and left tailed.

The test statistic is,

Z = (Xbar - mu) / (sd/sqrt(n))

Z = (-2.1 - 0) / (4.8/sqrt(40))

Z = -2.7670

Now we have to find critical value :

Critical value by using EXCEL is,

=NORMSINV(probability)

where, probability = alpha

critical value = -1.645

Here t < critical value,

reject H0 at 5% level of significance.

Conclusion : the mean weight change is less than zero.