Question

Given the sample mean = 23.375, sample standard deviation = 5.29, and N = 40 for the low income group, Test the claim that the mean nickel diameter drawn by children in the low income group is greater than 21.21 mm. Test at the 0.01 significance level.
a) Identify the correct alternative hypothesis:
A. p > 21.21
B. p < 21.21
C. p = 21.21
D. μ < 21.21
E. μ > 21.21
F. μ = 21.21
Give all answers correct to 3 decimal places
b) The test statistic value is:_______
c) Using the Traditional method, the critical value is:_______

Answer 1

Answer:

Step-by-step explanation:

a. To identify the alternative hypothesis, we have to examine the claim

The claim is that the mean nickel diameter drawn by children in the low income group is greater than 21.21 mm

Thus, alternative hypothesis is μ > 21.21

b. The test statistics is

z score = x - u /(sd/√n)

Where x (sample mean) is 23.375, u is pop. mean is 21.21, sd is 5.29 and n (sample size) is 40

z = 23.375 - 21.21 /(5.29/√40)

z = 2.165 / (5.29/6.3246)

z = 2.165/0.8364

z = 2.588

c. The critical value is

Alpha for this case study is 0.01. Then the critical probability is 1 - (alpha/2) =

1 - (0.01/2) = 1 - 0.005 = 0.995

To express the critical value as a z score, find the z score corresponding to the critical probability using the z table. Which is 0.8389.