Question

A researcher knows that the weights of 6-year-olds are normally distributed with U = 20.9 kg and SD= 3.2. She suspects that children in poverty-stricken regions are undernourished and therefore underweight. With a sample of n = 16 children, the researcher obtains a sample mean of M = 18.3. Use a one-tailed test with SD= .01 to determine if the weights for this sample are significantly lower than what would be expected for the regular population of 6-year-olds.

Answer 1

Solution:

Given:   the weights of 6-year-olds are normally distributed with 20.9 kg and   3.2 kg.

Sample size =n = 16

Sample mean = M = 18.3

Level of significance =

We have to test if the weights for this sample are significantly lower than what would be expected for the regular population of 6-year-olds.

Step 1) State H0 and H1:

Vs

Step 2) Test statistic:

Step 3) z critical value:

Since this is left tailed test , look in z table for or its closest area and find z value.

Area 0.0099 is closest to 0.0100 and it corresponds to -2.3 and 0.03

thus z critical value = -2.33

Step 4) Decision Rule:
Reject null hypothesis ,if z  test statistic value < z critical value= -2.33, otherwise we fail to reject H0.

Since z  test statistic value = -3.25 < z critical value= -2.33, we reject null hypothesis H0.

Step 5) Conclusion:

At 0.01 level of significance , we have sufficient evidence to conclude that: the weights for this sample are significantly lower than what would be expected for the regular population of 6-year-olds.

That is suspect of researcher that children in poverty-stricken regions are undernourished and therefore underweight is correct.