GBA306 Statistical M BUSINESS STATISTIC Chapter 12 Homework Question 6 (87) 6. 8

Question

GBA306 Statistical M BUSINESS STATISTIC Chapter 12 Homework Question 6 (87) 6. 8.57 points Exercise 12-25 Algo Consider the following sample data with mean and standard deviation of 17 0 and 7.4, respectively Use Table 3 Class Less than 10 10 up to 20 20 up to 30 30 or more reque 36 93 70 19 218 a. Using the goodness-of-fit test for normaity, specify the competing hypotheses in order to determine whether or not the data are normally distributed Ho: The data are normally distributed with a mean of 170 and a standard deviation of 7 4 : HA The data are not normally distributed with a mean of 17 0 and a standard deviation of 7.4 O Ho The data are not normally distributed with a mean of 17 0 and a standard deviation of 74, HA The data are normally distributed with a mean of 170 and a standard deviation ot 7 4 b. At the 1 0% significance level, what is the decision rule? (Round your answer to 3 decimal places.) Reject Ho if xay 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.) c. Test statistic Lenovo

Explanation / Answer

a)

Null and alternate hypothesis is as per option A

H0: given data follows normal distribution

Ha: given data does not follow normal distribution

b)

Reject H0 if chi-square > 11.3449 (Excel formula: =CHISQ.INV.RT(0.01,3))

c)

Using the central limit theorem we calculated the expected probabilities for the given classes. And further expected frequencies are calculated as pi*218.

In the below table, pi for the class - less than 10 is calculated as P(X<10) = P(z < (10 - 17)/7.4))

= P(z < -9459) = 0.1712

similarly, other probabilities are calculated

Test statistic, chi-square = 14.3939

Class Observed Frequency(Oi) pi Expected Frequency(Ei) (Oi - Ei)^2/Ei Less than 10 36 0.1721 37.5152 0.0612 10 up to 20 93 0.4853 105.8002 1.5486 20 up to 30 70 0.3031 66.0780 0.2328 30 or more 19 0.0395 8.6066 12.5513 Total 218 14.3939

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