Question

A researcher knows that the heights of 15-year old boys are normally distributed with μ = 67 inches and s = 3.8. She suspects that children living with families who tend to eat lots of processed foods will be shorter. With a sample of n = 16 children raised in processed-diet families, the researcher obtains a sample mean of M = 65 inches. With an a = .05, determine if the heights for this sample are significantly lower than what would be expected for the regular population of 15-year-old males.

1) Enter the critical Z-cutoff value for this test. If it is a two-tailed test, either the negative or positive cutoff values will provide the correct answer (please round to 2 decimal places).

2) Calculate the sample mean's Z-score.

3) Select the correct decision:

A) Reject the null. Children from processed food eating families have lower heights than other children.

B) Accept the null. There were no significant differences in children’s heights based on the diet of their family.

C) Accept the null. Children from processed food eating families have significantly different heights than other children.

D) Reject the null. There were no significant differences in children’s heights based on the diet of their family.

Answer 1

1)

This is left tailed test, for α = 0.05
Critical value of z is -1.64
Hence reject H0 if z < -1.645

2)

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (65 - 67)/(3.8/sqrt(16))
z = -2.11

3)

A) Reject the null. Children from processed food eating families have lower heights than other children.