Q1 A baseball player hit 59 home runs in a season Of the 59

Q1: A baseball player hit 59 home runs in a season. Of the 59 home runs, 19 went to right field, 18 went to right center field, 8 went to center field, 12 went to left center field, and 2 went to left field.

What is the probability that a randomly selected home run was hit to center field?

Was it unusual for this player to hit a home run to center field?

Q2: You suspect a 6-sided die to be loaded and conduct a probability experiment by rolling the die 400 times. The outcome of the experiment is listed in the following table.

Value of Die

Frequency

Value of Die

Frequency

1

71

4

61

2

71

5

74

3

62

6

61

Do you think the die is loaded?

Solution

1)

probability player hit a home run to center field

= 18 + 8 + 12 / 59

= 64.41%

No its not unusual to hit home run to center field

2)

we find chi-square test statistic

expected outcome for each value of die = 1/6 * 400 = 200/3 = 67

test statistic = sumof [ (observed-expected)^2/expected]

= (71- 67)^2/67 + (71-67)^2/67 + (62-67)^2/67 + (61-67)^2/67 + (74-67)^2/67 + + (61-67)^2/67

= 2.657

critical value = 11.07

since critical value is greater than test statistic

die is not loaded