Question

In: Statistics and Probability

The annual incomes of a random sample of 10 individuals in a certain city are given...

  1. The annual incomes of a random sample of 10 individuals in a certain city are given below. Construct at 95% confidence interval for the average yearly income of individuals in this city.

    65100, 52400, 32000, 33300, 72200, 39700, 39400, 42800, 54300, 68200,

Solutions

Expert Solution

the necessary calculation table :-

income (x) x2
65100 4238010000
52400 2745760000
32000 1024000000
33300 1108890000
72200 5212840000
39700 1576090000
39400 1552360000
42800 1831840000
54300 2948490000
68200 4651240000
sum=499400 sum=26889520000

sample size (n) = 10

[ for these values you can directly use any software or excel or your calculator ..i am just showing all calculations for your clarification]

degrees of freedom = (n-1) = (10-1) = 9

t critical value for alpha=0.05,df = 9, both tailed test be:-

[ using t distribution table ]

the  95% confidence interval for the average yearly income of individuals in this city is :-

* as nothing is mentioned i have rounded off the final answer to nearest whole number .

interpretation:-

we are 95% confident that the average yearly income of individuals in this city will be between 39412 and 60468.

*** if you have any doubt regarding the problem please write it in the comment box.if you are satisfied please give me a LIKE if possible...


Related Solutions

A poll is conducted in a certain city, regarding a certain referendum A random sample of...
A poll is conducted in a certain city, regarding a certain referendum A random sample of 100 shows that 62 are IN FAVOR of the referendum. (3)CONTINUED Please determine an 80% confidence interval for the proportion of the population in that city who ARE IN FAVOR of the referendum.
In a random sample of 100 persons with low incomes, 100 persons with average incomes, and...
In a random sample of 100 persons with low incomes, 100 persons with average incomes, and 100 persons with high incomes, there were, respectively, 40, 50, and 60 who love biking. (a) Use the 0.05 level of significance to test the null hypothesis θ1 = θ2 = θ3 = 0.5 (that the proportion of persons loving biking is 50% for all three income groups) against the alternative hypothesis that the three θ’s are not all equal to 0.5. In carrying...
The average annual rainfall in a particular city is 37.4 inches. In a random sample of...
The average annual rainfall in a particular city is 37.4 inches. In a random sample of the last 38 years, it was revealed that the average annual rainfall was 38.2 inches. The population standard deviation of the average annual rainfall in the particular city is 4.7 inches. At the 0.04 level of significance, can it be concluded that the average annual rainfall in the particular city is greater than 37.4 inches? Show your work to receive credit.
In a study of annual apartment rental costs in a city, a random sample of 50...
In a study of annual apartment rental costs in a city, a random sample of 50 apartments has a mean annual rental cost of $11,535 and a standard deviation of $975. Construct a 99% confidence interval for the mean annual apartment rental cost of all apartments in the city.                                                           [3 marks]
The unemployment rate in a certain city is 8.5%. A random sample of 100 people from...
The unemployment rate in a certain city is 8.5%. A random sample of 100 people from the labor force is drawn. Find the probability that the sample contains at least ten unemployed people.
The unemployment rate in a certain city is 8.5%. A random sample of 100 people from...
The unemployment rate in a certain city is 8.5%. A random sample of 100 people from the labor force is drawn. Find the probability that the sample contains at least ten unemployed people.
In a certain city, there are about one million eligible voters. A simple random sample of...
In a certain city, there are about one million eligible voters. A simple random sample of size 10,000 was chosen to study the relationship between gender and participation in the last election. The results were: In a certain city, there are about one million eligible voters. Men Women Voted 2499 3311 Didn't Vote 1722 2468 If we are testing for a relationship between gender and participation in the last election, what is the p-value and decision at the 5% significance...
A random sample of 31 residents in a particular city indicates an average annual income of...
A random sample of 31 residents in a particular city indicates an average annual income of $51,950 with a sample standard deviation of $7,785. Construct a 95% confidence interval to estimate the true average annual income for all residents in the city. Do not round intermediate calculations. Round your final answers to 2 decimal places. Omit the "$" sign. Lower bound for confidence interval =    dollars, Upper bound for confidence interval =  dollars.
1. A random sample of 10 drivers reported the below-average mileage in the city for their...
1. A random sample of 10 drivers reported the below-average mileage in the city for their cars. 18, 21, 24, 25, 25, 25, 25, 26, 29, & 31. The mean of the sample is 24.9 miles per gallon, with an associated standard deviation of about 3.6. Assuming the population mean =3.71. Find the 95% confidence interval for the average mileage of the cars for all of the drivers in the class.
1. A random sample of 64 second graders in a certain school district are given a...
1. A random sample of 64 second graders in a certain school district are given a standardized mathematics skills test. The sample mean score is 51.58. Assume the standard deviation for the population of test scores is 15. The nationwide average score on this test us 50. The school superintendent wants to know whether the second graders in her school district have greater math skills than the nationwide average. Perform the hypothesis test and compute the P value. Based on...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT