A municipality wishes to determine the average utility bill for its county's population. In a random sample of 100 customers,it was found that the sample average utility bill was $112.59. Assuming the population standard deviation is $18.53, findthe margin of error of the confidence interval with a 97% confidence level.Use the table of values below to assist you in determining the confidence coefficient. Round your margin of error to 2decimal places, as needed.1.881 1.9602.0542.170 2.326Provide your answer below:

Question
Asked Feb 27, 2019
A municipality wishes to determine the average utility bill for its county's population. In a random sample of 100 customers,
it was found that the sample average utility bill was $112.59. Assuming the population standard deviation is $18.53, find
the margin of error of the confidence interval with a 97% confidence level.
Use the table of values below to assist you in determining the confidence coefficient. Round your margin of error to 2
decimal places, as needed.
1.881 1.9602.0542.170 2.326
Provide your answer below:
help_outline

Image Transcriptionclose

A municipality wishes to determine the average utility bill for its county's population. In a random sample of 100 customers, it was found that the sample average utility bill was $112.59. Assuming the population standard deviation is $18.53, find the margin of error of the confidence interval with a 97% confidence level. Use the table of values below to assist you in determining the confidence coefficient. Round your margin of error to 2 decimal places, as needed. 1.881 1.9602.0542.170 2.326 Provide your answer below:

fullscreen
check_circleExpert Solution
Step 1

Margin of error:

Margin of error is a range of values that lie above and below the sample statistic of the confidence interval; it gives the percentage of number of points that differ in the obtained results from the population value.

Margin of error is calculated as the product of critical value and standard deviation or the product of critical value and standard error of the statistic.

The general formula for obtaining margin of error is,

fullscreen
Step 2

Obtain the critical value:

The required confidence level is 100*(1–α)% = 97%.

The required conditions for using standard normal distribution to estimate the confidence interval about mean is given below:

  • The population standard deviation σ must be known.
  • Either the sample size (n) must be greater than 30 or the population must be normally distributed.

Here, it is given that the sample size is 100 (which is greater than 30) and the population standard deviation is known.

From the given common z-values using standard normal distribution the critical value is obtained as 2.17 from the calculation given below:

fullscreen
Step 3

Find the margin of error of the confidence interval with 97% confidence level:

Given that, the population standard deviation is σ = 18.53,

The sample mean is x-bar = 112.59,

The sample size is n = 100,

The critical value is z(α/2) = z...

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour*

See Solution
*Response times may vary by subject and question
Tagged in

Math

Statistics

Hypothesis Testing

Related Statistics Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: 10 9 8 6 Frequency 5 4 3 2 1 0 to 9 10 to 19 20 to 29 30 to 39 40 to 49 50 to 59 The table above lis...

A: Frequency table:Frequency table represents the number of times each class repeats.The frequency of e...

question_answer

Q: After you determine the mean annual return, how do you find the standard deviation?

A: Click to see the answer

question_answer

Q: In a recent survey it was stated that Americans watch television on average four hours per day. Assu...

A: Hey, since there are multiple subparts posted, we will answer first three subparts. If you want any ...

question_answer

Q: Find the mean, the median, the mode, and the midrange, the range, variance, standard deviation, 65th...

A: Hello there! According to our policies can answer one question . As there are multiple questions in ...

question_answer

Q: A researcher wants to investigate whether mindfulness training improves ability for employees to not...

A: In an experiment the factor is an explanatory varible which is manipulated by the experimenter. It i...

question_answer

Q: The price to earnings ratio (P/E) is an important tool in financial work. A random sample of 14 larg...

A: (a) Level of significance:Level of significance (α) indicates the probability of rejecting null hypo...

question_answer

Q: There are six multiple-choice questions on an exam, each with three possible answers. (a) Determine ...

A: According to the given question, there are six multiple-choice questions on an exam, each with three...

question_answer

Q: In a study of 420,077 cell phone users, 107 subjects developed cancer of the brain or nervous system...

A: Given hypothesis test let p be the proportion of cellphone users develop cancer or brain or nervous ...

question_answer

Q: Directions: Draw the normal curve and shade in the specific region. Show formulas used and the subst...

A: Introduction:The normal distribution is a symmetric and mesokurtic continuous probability distributi...