/*! 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} Q2 Small Sample Weights of golden r... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q2 (page 272)

Small Sample Weights of golden retriever dogs are normally distributed. Samples of weights of golden retriever dogs, each of size n = 15, are randomly collected and the sample means are found. Is it correct to conclude that the sample means cannot be treated as being from a normal distribution because the sample size is too small? Explain.

Short Answer

Expert verified

It is incorrect to conclude that the sample means cannot be treated as values from a normal distribution as the sample size is too small because it is mentioned that the population of weights of golden retriever dogs is normally distributed.

Thus, all samples selected from this population will be normally distributed.

Step by step solution

01

Given information

It is given that weights of golden retriever dogs are normally distributed and samples of size equal to 15 are extracted from this population.

02

Requirements under which sample means is said to follow a normal distribution

One of the following requirements must be fulfilled for the computed sample mean to be treated as a value from a normally distributed population.

  • It should be clearly stated that the sample is extracted from the normally distributed population.
  • The sample size should be greater than 30.

Here, it is given that the population of weights of golden retriever dogs is normally distributed. That is, one of the requirements is met.

Thus, the sample means can be treated as being from a normal population as all the samples will be normally distributed.

It is incorrect to conclude that the sample means cannot be treated as being from a normal distribution because the sample size is too small.

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

Quarters After 1964, quarters were manufactured so that their weights have a mean of5.67 g and a standard deviation of 0.06 g. Some vending machines are designed so that you canadjust the weights of quarters that are accepted. If many counterfeit coins are found, you cannarrow the range of acceptable weights with the effect that most counterfeit coins are rejectedalong with some legitimate quarters.

a. If you adjust your vending machines to accept weights between 5.60 g and 5.74 g, what percentage of legal quarters are rejected? Is that percentage too high?

b. If you adjust vending machines to accept all legal quarters except those with weights in the top 2.5% and the bottom 2.5%, what are the limits of the weights that are accepted?

In Exercises 7鈥�10, use the same population of {4, 5, 9} that was used in Examples 2 and 5. As in Examples 2 and 5, assume that samples of size n = 2 are randomly selected with replacement.

Sampling Distribution of the Sample Standard Deviation For the following, round results to three decimal places.

a. Find the value of the population standard deviation

b. Table 6-2 describes the sampling distribution of the sample mean. Construct a similar table representing the sampling distribution of the sample standard deviation s. Then combine values of s that are the same, as in Table 6-3 (Hint: See Example 2 on page 258 for Tables 6-2 and 6-3, which describe the sampling distribution of the sample mean.)

c. Find the mean of the sampling distribution of the sample standard deviation. d. Based on the preceding results, is the sample standard deviation an unbiased estimator of the population standard deviation? Why or why not?

Basis for the Range Rule of Thumb and the Empirical Rule. In Exercises 45鈥�48, find the indicated area under the curve of the standard normal distribution; then convert it to a percentage and fill in the blank. The results form the basis for the range rule of thumb and the empirical rule introduced in Section 3-2.

About______ % of the area is between z = -1 and z = 1 (or within 1 standard deviation of the mean).

Continuous Uniform Distribution. In Exercises 5鈥�8, refer to the continuous uniform distribution depicted in Figure 6-2 and described in Example 1. Assume that a passenger is randomly selected, and find the probability that the waiting time is within the given range.

Greater than 3.00 minutes

Mensa Membership in Mensa requires a score in the top 2% on a standard intelligence test. The Wechsler IQ test is designed for a mean of 100 and a standard deviation of 15, and scores are normally distributed.

a. Find the minimum Wechsler IQ test score that satisfies the Mensa requirement.

b. If 4 randomly selected adults take the Wechsler IQ test, find the probability that their mean

score is at least 131.

c. If 4 subjects take the Wechsler test and they have a mean of 132 but the individual scores are lost, can we conclude that all 4 of them are eligible for Mensa?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation
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.