A firm employs 189 junior accountants. In a random sample of 50 of these, the mean number of hours overtime billed in a particular week was 9.7, and the sample standard deviation was 6.2 hours. Find a 95\% confidence interval for the mean number of hours overtime billed per junior accountant in this firm that week.

UkusakazaL 2021-08-10 Answered
A firm employs 189 junior accountants. In a random sample of 50 of these, the mean number of hours overtime billed in a particular week was 9.7, and the sample standard deviation was 6.2 hours.
a. Find a 95% confidence interval for the mean number of hours overtime billed per junior accountant in this firm that week.
b. Find a 99% confidence interval for the total number of hours overtime billed by junior accountants in the firm during the week of interest.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

question2answer
Answered 2021-08-16 Author has 155 answers

Given data,
The number of employee is 189.
The mean of the overtime is 9.7.
The standard deviation of overtime is 6.2
The sample size is 50.
Step 1
a) A 95% confidence interval for the mean number of hours overtime,
Error margin =z0.052σn
=z0.00256.250
=1.96×0.8768
=1.72
The lower bound of the interval is,
L=μ Error
=9.71.72
=7.98
The upper bound of the interval is,
U=μ+ Error
=9.7+1.72
=11.42
Step 2
b) A 99% confidence interval for the mean number of hours overtime,
Error margin =z0.012σn
=z0.0056.250
=2.576×0.8768
=2.2586
The lower bound of the interval is,
L=μ Error
=9.72.2586
=7.4414
The upper bound of the interval is,
U=μ+ Error
=9.7+2.2586
=11.9586

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-03-09

In a study of the accuracy of fast food​ drive-through orders, Restaurant A had 298 accurate orders and 51 that were not accurate. a. Construct a 90​% confidence interval estimate of the percentage of orders that are not accurate. b. Compare the results from part​ (a) to this 90​% confidence interval for the percentage of orders that are not accurate at Restaurant​ B: 0.127<p<0.191. What do you​ conclude? a. Construct a 90​% confidence interval. Express the percentages in decimal form. ___

asked 2021-08-03
A simple random sample of 60 items resulted in a sample mean of 80. The population standard deviation is σ=15
a) Compute the 95% confidence interval for the population mean. Round your answers to one decimal place.
b) Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean. Round your answers to two decimal places.
c) What is the effect of a larger sample size on the interval estimate?
Larger sample provides a-Select your answer-largersmallerItem 5 margin of error.
asked 2020-12-27
Consider the next 1000 98% Cis for mu that a statistical consultant will obtain for various clients. Suppose the data sets on which the intervals are based are selected independently of one another. How many of these 1000 intervals do you expect to capture the corresponding value of μ?
What isthe probability that between 970 and 990 of these intervals conta the corresponding value of ? (Hint: Let
Round your answer to four decimal places.)
‘the number among the 1000 intervals that contain What king of random variable s 2) (Use the normal approximation to the binomial distribution
asked 2021-08-09

A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before​ treatment, 13 subjects had a mean wake time of 101.0 min. After​ treatment, the 13 subjects had a mean wake time of 94.6 min and a standard deviation of 24.9 min. Assume that the 13 sample values appear to be from a normally distributed population and construct a 95% confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of 101.0 min before the​ treatment? Does the drug appear to be​ effective?
Construct the 95% confidence interval estimate of the mean wake time for a population with the treatment.
min<μ<min ​(Round to one decimal place as​ needed.)
What does the result suggest about the mean wake time of 101.0 min before the​ treatment? Does the drug appear to be​ effective?
The confidence interval ▼ does not include| includes the mean wake time of 101.0 min before the​ treatment, so the means before and after the treatment ▼ could be the same |are different. This result suggests that the drug treatment ▼ does not have | has a significant effect.

asked 2022-04-24
If we calculate the probability P(A) that event A will occur and obtain the corresponding confidence interval
z_{1}ZSK. If I have n trials, the expected number of trials that will result in event A is nP(A). But what then is the confidence interval z2 for this expected number of events A?
asked 2021-05-09

The two intervals (114.4, 115.6) and (114.1, 115.9) are confidence intervals (computed using the same sample data) for μ= true average resonance frequency (in hertz) for all tennis rackets of a certain type.
a. What is the value of the sample mean resonance frequency?
b. The confidence level for one of these intervals is 90%90%and for the other it is 99%99%. Which is which, and how can you tell?

asked 2021-01-31
Sketch a graph of y=2xon[1,2] and use geometry to find the exact value of function given
122x dx