- Grade distribution: A statistics teacher claims that, on theaverage, 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 randomsample of 100 students were recorded. The following tablepresents the results.в сD F5 4GradeAObserved294220a. How many of the students in the sample got an A? Howmany got an F?b. Compute the expected frequencies.c. Which grades were given more often than expected?Which grades were given less often thanexpected?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 inwhich players try to guess the numbers that will turn up in adrawing of numbered balls. One of the balls drawn is the MegaBall. Matching the number drawn on the Mega Ball increasesones winnings. During a recent three-year period, the Mega Ballwas drawn from a collection of 15 balls numbered 1 through 15,and a total of 344 drawings were made. For the purposes of thisexercise, we grouped the numbers into five categories: 1-3, 4–6,and so on. If the lottery is fair, then the winning number isequally likely to occur in any category. Following are theobserved frequencies.Category1-34-67-910-1213–15Observed7364746271Source: www.usamega.coma. 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

Since you have asked multiple questions, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question. a. A sample of 100 students were recorded. From the sample 29 of the students got grade A and 4 f the students got grade F. Thus, 29 students in the sample got an A and 4 students in the sample got an F. b. The expected frequencies are, Grade Percent Expected Frequencies A 20 100×0.20=20 B 35 100×0.35=35 C 25 100×0.25=25 D 10 100×0.10=10 F 10 100×0.10=10 The expected frequencies are, Grade Expected Frequencies A 20 B 35 C 25 D 10 F 10c. Grade Observed (O) Expected Frequencies (E) A 29 20 B 42 35 C 20 25 D 5 10 F 4 10 It can be observed that, the observed grades A and B are more often than expected frequencies. Also, the observed grades C, D and F are less often than expected frequencies. Thus, grades A and B are given more often than expected, grades C, D and F are less often than expected.d. The chi-square test statistic is, χ2=∑O-E2E=29-20220+42-35235+20-25225+5-10210+4-10210=4.05+1.40+1.00+2.50+3.60=12.55 Thus, χ2=12.55.e. For k different groups, the degrees of freedom for chi-square is, df=k-1=5-1=4 Thus, the degrees of freedom is 4.

Math

Statistics

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?

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?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

- 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

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