Consider the following sample data with mean and standard deviation of 18.5 and
ID: 3060535 • Letter: C
Question
Consider the following sample data with mean and standard deviation of 18.5 and 7.1, respectively. Use Table 3.
Using the goodness-of-fit test for normality, specify the competing hypotheses in order to determine whether or not the data are normally distributed.
Calculate the value of the test statistic. (Round the z value to 2 decimal places, all other intermediate values to at least 4 decimal places and final answer to 2 decimal places.)
Consider the following sample data with mean and standard deviation of 18.5 and 7.1, respectively. Use Table 3.
Explanation / Answer
a. Hypothesis are
H0: The data are normally distributed with a mean of 18.5 and a standard deviation of 7.1.
HA: The data are not normally distributed with a mean of 18.5 and a standard deviation of 7.1.
b. Reject X2df
Here dF = 4 -2 -1 = 3 and alpha = 0.10
X2df = 2.7055
Test statistic X2 = 2.913
(d) Here, X2df < X2 so we reject the null hypothesis Reject H0; the data are not normally distributed. Option A is correct.
Class Frequency Z Area Below Expected (O - E)^2/E < 10 26 -1.1972 0.1156 21.27 1.050 10 < x < 20 85 0.2113 0.4680 86.12 0.015 20 < x <30 60 1.6197 0.3637 66.92 0.715 30 > x 13 infinity 0.0526 9.69 1.133 Sum 184 1 184 2.913 Mean 18.5 Std. Dev. 7.1