29. Testing Goodness-of-Fit with a Binomial Distribution An observed frequency distribution is as follows: p 5 1> s1 1 2d, z 5 sp 2 pd>2pq>n

29. Testing Goodness-of-Fit with a Binomial Distribution An observed frequency distribution is as follows:

pˆ 5 ƒ1> sƒ1 1 ƒ2d, z 5 spˆ 2 pd>2pq>n sƒ1 1 ƒ2d>2.

Leading digit 1 2 3 4 5 6 7 8 9 Frequency 72 23 26 20 21 18 8 8 4 Number of successes 0 1 2 3 Frequency 89 133 52 26

a. Assuming a binomial distribution with n 5 3 and use the binomial probability formula to find the probability corresponding to each category of the table.

b. Using the probabilities found in part (a), find the expected frequency for each category.

c. Use a 0.05 significance level to test the claim that the observed frequencies fit a binomial distribution for which n 5 3 and 30. Testing Goodness-of-Fit with a Normal Distribution An observed frequency distribution of sample IQ scores is as follows:

p 5 1>3.

p 5 1>3, Less than More than IQ score 80 80–95 96–110 111–120 120 Frequency 20 20 80 40 40 continued 606 Chapter 11 Multinomial Experiments and Contingency Tables

a. Assuming a normal distribution with m 5 100 and s 5 15, use the methods given in Chapter 6 to find the probability of a randomly selected subject belonging to each class. (Use class boundaries of 79.5, 95.5, 110.5, and 120.5.)

b. Using the probabilities found in part (a), find the expected frequency for each category.

c. Use a 0.01 significance level to test the claim that the IQ scores were randomly selected from a normally distributed population with m 5 100 and s 5 15.