Question

In: Math

The personnel department of a large corporation wants to estimate the family dental expenses of its...

The personnel department of a large corporation wants to estimate the family dental expenses of its employees to determine the feasibility of providing a dental insurance plan. A random sample of 12 employees in 2004 reveals the following dental expenses (in dollars): 115, 370, 250, 93, 540, 225, 177, 425, 318, 182, 275, and 228. The sample mean is ___________. Construct a 95% confidence interval estimate of the mean family dental expenses for all employees of this corporation. The upper boundary/limit is _________ and the lower boundary/limit is ________. (keep two decimal points).

Solutions

Expert Solution

Solution:

x x2
115 13225
370 136900
250 62500
93 8649
540 291600
225 50625
177 31329
425 180625
318 101124
182 33124
275 75625
228 51984
x=3198 x2=1037310

The sample mean is

Mean     = (x / n) )

= (115,+370+ 250+ 93,+540+ 225+ 177+ 425+ 318+ 182+ 275+228 / 12)

= 3198 / 12

= 266.5

Mean = 266.5

The sample standard is S

  S = ( x2 ) - (( x)2 / n ) n -1

= (1037310( (3198 )2 / 12 ) 11

   = (1037310 - 852267 / 11)

= (185043/ 11)

= 16822.0909

= 129.7

The sample standard is = 129.7

Degrees of freedom = df = n - 1 = 12 - 1 = 11

At 95% confidence level the t is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,11 = 2.201

Margin of error = E = t/2,df * (s /n)

= 2.201 * (129.7 / 12)

= 82.41

Margin of error = 82.41

The 95% confidence interval estimate of the population mean is,

- E < < + E

266.5 - 82.4 1< <266.5 + 82.41

184.09 < < 348.91

The upper boundary/limit = 348.91

The lower boundary/limit =184.09

milcah answered 1 year ago
Next > < Previous

Related Solutions

The personnel department of a large corporation wants to estimate the family dental expenses of its...
The personnel department of a large corporation wants to estimate the family dental expenses of its employees to determine the feasibility of providing a dental insurance plan. A random sample of 12 employees reveals the following family dental expenses (in dollars): 115, 370, 250, 593, 540, 225, 177, 425, 318, 182, 275, and 228. Construct a 97% confidence interval estimate for the standard deviation of family dental expenses for all employees of this corporation
The marketing director of a large department store wants to estimate the average number of customers...
The marketing director of a large department store wants to estimate the average number of customers who enter the store every five minutes. She randomly selects five-minute intervals and counts the number of arrivals at the store. She obtains the figures 56, 32, 41, 49, 56, 80, 42, 29, 32, and 70. The analyst assumes the number of arrivals is normally distributed. Using these data, the analyst computes a 95% confidence interval to estimate the mean value for all five-minute...
The marketing director of a large department store wants to estimate the average number of customers...
The marketing director of a large department store wants to estimate the average number of customers who enter the store every five minutes. She randomly selects five-minute intervals and counts the number of arrivals at the store. She obtains the figures 56, 32, 41, 49, 56, 80, 42, 29, 32, and 70. The analyst assumes the number of arrivals is normally distributed. Using these data, the analyst computes a 95% confidence interval to estimate the mean value for all five-minute...
The marketing director of a large department store wants to estimate the average number of customers...
The marketing director of a large department store wants to estimate the average number of customers who enter the store every five minutes. She randomly selects five-minute intervals and counts the number of arrivals at the store. She obtains the figures 52, 32, 41, 49, 56, 80, 46, 29, 32, and 71. The analyst assumes the number of arrivals is normally distributed. Using these data, the analyst computes a 95% confidence interval to estimate the mean value for all five-minute...
The marketing director of a large department store wants to estimate the average number of customers...
The marketing director of a large department store wants to estimate the average number of customers who enter the store every five minutes. She randomly selects five-minute intervals and counts the number of arrivals at the store. She obtains the figures 51, 32, 41, 47, 56, 80, 49, 29, 32, and 80. The analyst assumes the number of arrivals is normally distributed. Using these data, the analyst computes a 95% confidence interval to estimate the mean value for all five-minute...
The personnel department of ZTel, a large communications company, is reconsidering its hiring policy. Each applicant...
The personnel department of ZTel, a large communications company, is reconsidering its hiring policy. Each applicant for a job must take a standard exam, and the hire or no-hire decision depends at least in part on the result of the exam. The scores of all applicants have been examined closely. They are approximately normally distributed with mean 500 and standard deviation 50. The current hiring policy occurs in two phases. The 1st phase separates all applicants into three categories: automatic...
A large​ family-held department store had the business objective of improving its response to complaints. The...
A large​ family-held department store had the business objective of improving its response to complaints. The variable of interest was defined as the number of days between when the complaint was made and when it was resolved. Data were collected from 40 complaints that were made in the last year. Use the data to complete parts​ (a) through​ (d) below. 47 13 8 27 43 159 17 49 20 3 105 19 3 64 88 22 30 120 49 102...
A personnel manager for a large corporation feels that there may be a relationship between absenteeism,...
A personnel manager for a large corporation feels that there may be a relationship between absenteeism, age and life status (single, married, divorced and other) of workers. He would like to develop a model to predict the number of days absent during a calendar year for workers using the independent variables above. A random sample of 20 workers was selected with the results presented below. Days Absent       Age       Life Status 15 27 Single 40 61 Divorced 10 37 Married 18...
4. The department of HR at the University of Michigan wants to estimate the amount of...
4. The department of HR at the University of Michigan wants to estimate the amount of an annual healthcare premium needed for an Assistant Professor as part of a new recruiting program. In a sample of 50 Assistant Professors, they found that the average yearly premium needed is $16,000 with a standard deviation of $3,500. (a) What is the population mean? What is the best estimate of the population mean? (b) Develop an 90% confidence interval for the population mean....
The personnel director of a large corporation determines the keyboarding speed, on certain standard materials, of...
The personnel director of a large corporation determines the keyboarding speed, on certain standard materials, of a random sample of secretaries from her company. She wants to know whether the keyboarding speed of secretaries at her company is different from the national mean of 50, with a standard deviation of 5. She conducts her study and finds a mean of 48 for 20 secretaries. Use the .05 level of significance to answer her question. 1. What are the null and...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT