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Chapter 8: Q. T8.13 (page 549)

A milk processor monitors the number of bacteria per milliliter in raw milk received at the factory. A random sample of 10one-milliliter specimens of milk supplied by one producer gives the following data:

Construct and interpret a 90% confidence interval for the population mean 渭.

Short Answer

Expert verified

The confidence interval is(4794.4,5105.6).

Step by step solution

01

Step 1. Given information

The data set is:

02

Step 2. Formula Used

The formula to compute the confidence interval is:

x炉-t伪2.n-1脳sn<渭<x炉+t伪2.n-1脳sn

03

Step 3. Calculation

Follow the provided steps of Minitab to compute the required confidence interval:

  1. Enter the data set in Minitab sheet.
  2. Click on Stat > Basic Statistics > 1-Sample t
  3. Select Sample in column.
  4. Click on options and enter 90%in confidence level.
  5. Click OK.

The obtained output is:

Hence, the required confidence interval is (4794.4,5105.6)

The obtained confidence interval shows that there is 90%probability that the mean number of bacteria per millimeter in raw milk lies between47.94.4 and5105.6.

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Most popular questions from this chapter

How confident? The figure shows the result of taking 25SRSs from a Normal population and constructing a confidence interval for the population mean using each sample. Which confidence level鈥攔ole="math" localid="1654197644211" 80%,90%,95%,or99%鈥攄o you think was used? Explain your reasoning.

Blood pressure A medical study finds that x炉=114.9and sx=9.3

for the seated systolic blood pressure of the 27randomly selected adults. What is the standard error of the mean? Interpret this value in context.

You have measured the systolic blood pressure of an SRS of 25company employees. A 95%confidence interval for the mean systolic blood pressure for the employees of this company is (122,138). Which of the following statements is true?

a. 95%of the sample of employees have a systolic blood pressure between 122 and 138.

b. 95%of the population of employees have a systolic blood pressure between 122and138.

c. If the procedure were repeated many times, 95%of the resulting confidence intervals would contain the population mean systolic blood pressure.

d. If the procedure were repeated many times, 95%of the time the population mean systolic blood pressure would be between 122and 138.

e. If the procedure were repeated many times, 95%of the time the sample mean systolic blood pressure would be between 122and138.

More cheating Refer to Exercise 36. Calculate and interpret the standard error of p^for these data.

Batteries A company that produces AA batteries tests the lifetime of a randomsample of 30 batteries using a special device designed to imitate real-world use. Based onthe testing, the company makes the following statement: 鈥淥ur AA batteries last an average of 430 to 470 minutes, and our confidence in that interval is 95%.鈥�36

a. Determine the point estimate, margin of error, standard error, and sample standard

deviation.

b. A reporter translates the statistical announcement into 鈥減lain English鈥� as follows: 鈥�95% of this company鈥檚 AA batteries last between 430 and 470 minutes.鈥� Comment on this interpretation.

c. Your friend, who has just started studying statistics, claims that there is a 95% probability that the mean lifetime will fall between 430 and 470 minutes. Do you agree? Explain your reasoning.

d. Give a statistically correct interpretation of the confidence level that could be published in a newspaper report.
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