1. Before the start of the Winter Olympics, it was expected that the percentages of medals awarded to the top contenders to be as follows.

##         Country Percentages
## 1 United States         25%
## 2       Germany         22%
## 3        Norway         18%
## 4       Austria         14%
## 5        Russia         11%
## 6        France         10%

Midway through the Olympics, of the 120 medals awarded, the following distribution was observed.

##         Country Number_of_Medals
## 1 United States               33
## 2       Germany               36
## 3        Norway               18
## 4       Austria               15
## 5        Russia               12
## 6        France                6

We want to test to see if there is a significant difference between the expected and actual awards given at 95% confidence.

Ans.

Number_of_Medals =  c(33,36,18,15,12,6)
res <- chisq.test(Number_of_Medals, p =c(0.25,0.22,0.18,0.14,0.11,0.10) )
res

## 
##  Chi-squared test for given probabilities
## 
## data:  Number_of_Medals
## X-squared = 7.6929, df = 5, p-value = 0.174

There is not enough evidence of significant difference between the expected and actual awards given at 95% confidence.

2. A medical journal reported the following frequencies of deaths due to cardiac arrest for each day of the week:

##        Week Number_of_Cardiac_Deaths
## 1    Monday                       40
## 2   Tuesday                       17
## 3 Wednesday                       16
## 4  Thursday                       29
## 5    Friday                       15
## 6  Saturday                       20
## 7    Sunday                       17

We want to determine whether the number of deaths is uniform over the week at 95% confidence.

Ans.

Number_of_Cardiac_Deaths =  c(40,17,16,29,15,20,17)
res <- chisq.test(Number_of_Cardiac_Deaths, p =c(1/7,1/7,1/7,1/7,1/7,1/7,1/7) )
res

## 
##  Chi-squared test for given probabilities
## 
## data:  Number_of_Cardiac_Deaths
## X-squared = 23.273, df = 6, p-value = 0.0007101

There is enough evidence that the number of deaths is not uniform over the week at 95% confidence.

3. Before the presidential debates, it was expected that the percentages of registered voters in favor of various candidates would be as follows.

##     Candidate Percentages
## 1   Democrats         48%
## 2 Republicans         38%
## 3 Independent          4%
## 4   Undecided         10%

After the presidential debates, a random sample of 1200 voters showed that 540 favored the Democratic candidate; 480 were in favor of the Republican candidate; 40 were in favor of the Independent candidate, and 140 were undecided. We want to see if the proportion of voters has changed at 95%.

Ans.

Number_of_voters =  c(540,480,40,140)
res <- chisq.test(Number_of_voters, p =c(0.48,0.38,0.04,0.10) )
res

## 
##  Chi-squared test for given probabilities
## 
## data:  Number_of_voters
## X-squared = 8.1798, df = 3, p-value = 0.04244

There is enough evidence that the proportion of voters has changed at 95% confidence.

4.Last school year, in the school of Business Administration, 30% were Accounting majors, 24% Management majors, 26% Marketing majors, and 20% Economics majors. A sample of 300 students taken from this year’s students of the school showed the following number of students in each major:

##       Majors Number_of_Majors
## 1 Accounting               83
## 2 Management               68
## 3  Marketing               85
## 4  Economics               64

We want to see if there has been a significant change in the number of students in each major at 95% confidence.

Ans.

Number_of_Majors =  c(83,68,85,64)
res <- chisq.test(Number_of_Majors, p =c(0.30,0.24,0.26,0.20) )
res

## 
##  Chi-squared test for given probabilities
## 
## data:  Number_of_Majors
## X-squared = 1.6615, df = 3, p-value = 0.6455

There is not enough evidence of a significant change in the number of students in each major

5.The personnel department of a large corporation reported sixty resignations during the last year. The following table groups these resignations according to the season in which they occurred:

##   Season Number_of_resignations
## 1 Winter                     10
## 2 Spring                     22
## 3 Summer                     19
## 4   Fall                      9

Test to see if the number of resignations is uniform over the four seasons at 95% confidence

Number_of_resignations=  c(10,22,19,9)
res <- chisq.test(Number_of_resignations, p =c(0.25,0.25,0.25,0.25) )
res

## 
##  Chi-squared test for given probabilities
## 
## data:  Number_of_resignations
## X-squared = 8.4, df = 3, p-value = 0.03843

There is enough evidence to infer that the number of resignations is not uniform over the four seasons at 95% confidence.