/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q19 Confidence Intervals. In Exercis... [FREE SOLUTION] | 91影视

91影视

Confidence Intervals. In Exercises 9鈥24, construct the confidence interval estimate of the mean. In Exercises 2-19,Mercury in SushiAn FDA guideline is that themercury in fish should be below 1 part per million (ppm). Listed below are the amounts of mercury (ppm) found in tuna sushi sampled at different stores in New York City. The study was sponsored by the New York Times, and the stores (in order) are D鈥橝gostino, Eli鈥檚 Manhattan, Fairway, Food Emporium, Gourmet Garage, Grace鈥檚 Marketplace, and Whole Foods. Construct a 98% confidence interval estimate of the mean amount of mercury in the population. Does it appear that there is too much mercury in tuna sushi?

0.56 0.75 0.10 0.95 1.25 0.54 0.88

Short Answer

Expert verified

The 98% confidence interval of the population mean amount of mercury in tuna sushi is equal to (0.287 ppm, 1.151 ppm)

Since there are possibilities of the mean amount of mercury exceeding 1 ppm, which is the safe value as per FDA guidelines, it can be said that there is too much mercury in tuna sushi.

Step by step solution

01

Given information

The amounts of mercury present in tuna sushi are given for 7 different stores in New York.

02

Calculation of  the sample mean 

Let x represent the amount of mercury present in tuna sushi.

The mean is computed below:

x=i=1nxin=0.56+0.75+...+0.887=0.719

Therefore, the sample mean amount of mercury in tuna sushi is 0.719 ppm.

03

Calculation of the sample standard deviation

The standard deviation is computed using the given formula:

s=i=1n(xi-x)2n-1=0.56-0.7192+0.75-0.7192+...+0.88-0.71927-1=0.366

Therefore, the standard deviation of the amount of mercury is 0366 ppm.

04

Calculation of the critical value  

The degrees of freedom are computed as follows:

n-1=7-1=6

The confidence level is 98%. Thus, the level of significance is equal to 0.02.

Referring to the t distribution table, the critical value of t2with 6 degrees of freedom at a 0.02 level of significance is equal to 3.1427.

05

Calculation of the margin of error

The margin of error is computed as follows:

E=t2sn=3.14270.3667=5.198

Therefore the margin of error is 5.198.

06

Calculation of the confidence interval

The confidence interval for the population mean is computed below:

x-E<<x+E0.719-0.432<<0.719+0.4320.287<<1.151

The 98% confidence interval of the population mean amount of mercury in tuna sushi is equal to (0.287 ppm, 1.151 ppm).

07

Analysis of the amount of mercury

As per FDA,the amount of mercury in fish should be below 1 ppm.

Upon observing the confidence interval, the mean amount of mercury can hold values greater than 1 ppm.

Therefore, it can be said that the amount of mercury in tuna sushi is high.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Normality Requirement What does it mean when we say that the confidence interval methodsof this section are robust against departures from normality?

Sample Size. In Exercises 29鈥36, find the sample size required to estimate the population mean.

Mean Grade-Point Average Assume that all grade-point averages are to be standardized on a scale between 0 and 4. How many grade-point averages must be obtained so that the sample mean is within 0.01 of the population mean? Assume that a 95% confidence level is desired. If we use the range rule of thumb, we can estimate to be,

=range4=4-04=1

Does the sample size seem practical?

Critical Thinking. In Exercises 17鈥28, use the data and confidence level to construct a confidence interval estimate of p, then address the given question.

Medication UsageIn a survey of 3005 adults aged 57 through 85 years, it was found that 81.7% of them used at least one prescription medication (based on data from 鈥淯se of Prescription and Over-the-Counter Medications and Dietary Supplements Among Older Adults in the United States,鈥 by Qato et al.,Journal of the American Medical Association,Vol. 300, No. 24).

a.How many of the 3005 subjects used at least one prescription medication?

b.Construct a 90% confidence interval estimate of thepercentageof adults aged 57 through 85 years who use at least one prescription medication.

c.What do the results tell us about the proportion of college students who use at least one prescription medication?

Genes Samples of DNA are collected, and the four DNA bases of A, G, C, and T are codedas 1, 2, 3, and 4, respectively. The results are listed below. Construct a 95% confidence intervalestimate of the mean. What is the practical use of the confidence interval?

2 2 1 4 3 3 3 3 4 1

Celebrity Net Worth Listed below are the amounts of net worth (in millions of dollars) of these ten wealthiest celebrities: Tom Cruise, Will Smith, Robert De Niro, Drew Carey, George Clooney, John Travolta, Samuel L. Jackson, Larry King, Demi Moore, and Bruce Willis. Construct a 98% confidence interval. What does the result tell us about the population of all celebrities? Do the data appear to be from a normally distributed population as required?

250 200 185 165 160 160 150 150 150 150

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.