Consider the following sample data with mean and standard deviation of 18.1 and
ID: 3355394 • Letter: C
Question
Consider the following sample data with mean and standard deviation of 18.1 and 7.4, respectively. Use Table 3 Class Less than 10 10 up to 20 20 up to 30 30 or more Frequency 69 13 n = 203 a. Using the goodness-of-fit test for normality, specify the competing hypotheses in order to determine whether or not the data are normally distributed O Ho. The data are normally distributed with a mean of 18.1 and a standard deviation of 7.4.; HA. The data are not normally distributed with a mean of 18.1 and a standard deviation of 7.4 Ho: The data are not normally distributed with a mean of 18.1 and a standard deviation of 7.4: HA The data are normally distributed with a mean of 18.1 and a standard deviation of 7.4 b. At the 1.0% significance level, what is the decision rule? (Round your answer to 3 decimal places.) Reject Ho if > c. 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.) Test statistic d. What is the conclusion? Do not reject Ho; the data are normally distributed Reject Ho: the data are not normally distributed Reject Ho, the data are normally distributed Do not reject Ho; the data are not normally distributedExplanation / Answer
a) Ho the data are normally distributed......................
b) degree of freedom =categories-1 =4-1 =3
for 3 df and 0.01 level critical value =11.345
test statisitc =1.80
d) do not reject Ho: the data are normally distributed
mean = 18.1 std deviation = 7.4 degree of freedom = k-m-1 = 3 Class Limits observed Normal Normal Expected 2=(O-E)2/E lower Upper Bin frequency(O) probabilty probabilty(p) frequency(E=p*O) - 10 -10 33 P(X<10) 0.1368 27.780 0.981 10 - 20 10-20 88 P(10<X<20) 0.4645 94.287 0.419 20 - 30 20-30 69 P(20<X<30) 0.3448 69.990 0.014 30 - inf 30-inf 13 P(30<X<inf) 0.0539 10.943 0.387 Total 203 1 203 1.801