Log In Start studying!

Select your language

Suggested languages for you:

Americas

English (US)

Europe

Q 16.

Expert-verified

The Practice of Statistics for AP Examination

Found in: Page 507

Book edition 6th

Author(s) Daren Starnes, Josh Tabor

Pages 837 pages

ISBN 9781319113339

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later

Short Answer

How confident? The figure shows the result of taking $25$ SRSs from a Normal population and constructing a confidence interval for the population mean using each sample. Which confidence level— $80 %, 90 %, 95 %, or 99 %$ —do you think was used? Explain your reasoning.

Confidence Level of $99 %$ is used.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given Information

We are given that

Step 2: Determining Confidence Level Used

Confidence Level is calculated as $\frac{25}{25} = 1$

$100 %$

Red line implies those sample means which have no true population mean.
There are zero samples among given $25$ samples not containing true proportion.
Hence, $25$ samples from $25$ samples has true population.
The confidence level which is closest is $99 %$

Most popular questions for Math Textbooks

Willows in Yellowstone Writers in some fields summarize data by giving x ̄ and its

standard error rather than $\bar{x} and S_{X}$ .Biologists studying willow plants in Yellowstone National Park reported their results in a table with columns labeled $\bar{x} and S_{X}$ The table entry for the heights of willow plants (in centimeters) in one region of the park was $61.55 \pm 19.03$ . The researchers measured a total of $23$ plants.

a. Find the sample standard deviation $s_{x}$ for these measurements.

b. A hasty reader believes that the interval given in the table is a $95 %$ confidence interval for the mean height of willow plants in this region of the park. Find the actual confidence level for the given interval.

After deciding on a $95 %$ confidence level, the researcher is deciding between a sample of size $n = 500$ and a sample of size $n = 1000$ . Compared with using a sample size of $n = 500$ , a confidence interval based on a sample size of $n = 1000$ will be

a. narrower and would involve a larger risk of being incorrect.

b. wider and would involve a smaller risk of being incorrect.

c. narrower and would involve a smaller risk of being incorrect.

d. wider and would involve a larger risk of being incorrect.

e. narrower and would have the same risk of being incorrect.

The Gallup Poll interviews 1600 people. Of these, 18% say that they jog regularly. The news report adds: “The poll had a margin of error of plus or minus three percentage points at a 95% confidence level.” You can safely conclude that

a. 95% of all Gallup Poll samples like this one give answers within ±3% of the true population value.

b. the percent of the population who jog is certain to be between 15% and 21%.

c. 95% of the population jog between 15% and 21% of the time.

d. we can be 95% confident that the sample proportion is captured by the confidence interval.

e. if Gallup took many samples, 95% of them would find that 18% of the people in the sample jog.

Got shoes? The class in Exercise 1 wants to estimate the variability in the number of pairs

of shoes that female students have by estimating the population standard deviation $σ$ .

t time When constructing confidence intervals for a population mean, we almost always use critical values from a t distribution rather than the standard Normal distribution.

a. When is it necessary to use a t critical value rather than a z critical value when constructing a confidence interval for a population means?

b. For a particular level of confidence, explain what happens to the t critical values as Page Number: 548 the degrees of freedom increase.

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free