Grade distribution: A statistics teacher claims that, on the average, 20% of her students get a grade of A, 35% get a B, 25% get a C, 10% get a D, and 10% get an F. The grades of a random sample of 100 students were recorded. The following table presents the results. A BC D F 5 4 Grade Observed 29 42 20 a. How many of the students in the sample got an A? How many got an F? b. Compute the expected frequencies. c. Which grades were given more often than expected? Which grades were given less often than expected? d. What is the value of x2? e. How many degrees of freedom are there?

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- Grade distribution: A statistics teacher claims that, on the
average, 20% of her students get a grade of A, 35% get a B, 25%
get a C, 10% get a D, and 10% get an F. The grades of a random
sample of 100 students were recorded. The following table
presents the results.
в сD F
5 4
Grade
A
Observed
29
42
20
a. How many of the students in the sample got an A? How
many got an F?
b. Compute the expected frequencies.
c. Which grades were given more often than expected?
Which grades were given less often than
expected?
d. What is the value of x2?
e. How many degrees of freedom are there?
Transcribed Image Text:- Grade distribution: A statistics teacher claims that, on the average, 20% of her students get a grade of A, 35% get a B, 25% get a C, 10% get a D, and 10% get an F. The grades of a random sample of 100 students were recorded. The following table presents the results. в сD F 5 4 Grade A Observed 29 42 20 a. How many of the students in the sample got an A? How many got an F? b. Compute the expected frequencies. c. Which grades were given more often than expected? Which grades were given less often than expected? d. What is the value of x2? e. How many degrees of freedom are there?
Is the lottery fair? Mega Millions is a multistate lottery in
which players try to guess the numbers that will turn up in a
drawing of numbered balls. One of the balls drawn is the Mega
Ball. Matching the number drawn on the Mega Ball increases
ones winnings. During a recent three-year period, the Mega Ball
was drawn from a collection of 15 balls numbered 1 through 15,
and a total of 344 drawings were made. For the purposes of this
exercise, we grouped the numbers into five categories: 1-3, 4–6,
and so on. If the lottery is fair, then the winning number is
equally likely to occur in any category. Following are the
observed frequencies.
Category
1-3
4-6
7-9
10-12
13–15
Observed
73
64
74
62
71
Source: www.usamega.com
a. Compute the expected frequencies.
b. Compute the value of x?
c. How many degrees of freedom are there?
d. Test the hypothesis that each of the categories is
Transcribed Image Text:Is the lottery fair? Mega Millions is a multistate lottery in which players try to guess the numbers that will turn up in a drawing of numbered balls. One of the balls drawn is the Mega Ball. Matching the number drawn on the Mega Ball increases ones winnings. During a recent three-year period, the Mega Ball was drawn from a collection of 15 balls numbered 1 through 15, and a total of 344 drawings were made. For the purposes of this exercise, we grouped the numbers into five categories: 1-3, 4–6, and so on. If the lottery is fair, then the winning number is equally likely to occur in any category. Following are the observed frequencies. Category 1-3 4-6 7-9 10-12 13–15 Observed 73 64 74 62 71 Source: www.usamega.com a. Compute the expected frequencies. b. Compute the value of x? c. How many degrees of freedom are there? d. Test the hypothesis that each of the categories is
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