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Chapter 12: Q.63 (page 737)

The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students鈥� attitudes toward school and study habits. Scores range from 0 to 200. The mean score for U.S. college students is about 115. A teacher suspects that older students have better attitudes toward school. She gives the SSHA to an SRS of 45 of the over 1000 students at her college who are at least 30 years of age. Check the conditions for carrying out a significance test of the teacher鈥檚 suspicion.

Short Answer

Expert verified

The simple random sample should be taken and satisfies the following condition:

1. The sample size should be atleast 30.

2. The population size must be greater than the sample size.

3. The sample size should be atleast greater than 10% of the actual population.

Step by step solution

01

Introduction

The distribution of frequencies of all possible results for a statistic of a population parameter refers to the sampling distribution of a given population.

02

Explanation

According to the central limit theorem, whenever the sample size is greater than 30, the sample mean distribution follows a normal distribution. In addition to this, the sample size should be less than 10%of the actual population.

It can be observed that the sample size given is equal to 45, that is, satisfies the normality condition.

Thus, the condition should be applied while choosing a simple random sample and satisfies the following condition:

1. The sample size should be atleast 30.

2. The population size must be greater than the sample size.

3. The sample size should be atleast greater than 10% of the actual population.

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Most popular questions from this chapter

A Harris Poll found that 54%of American adults don鈥檛 think that human beings developed from earlier species. The poll鈥檚 margin of error for 95%confidence was 3%. This means that ,

(a) There is a 95%chance that the interval (51%,57%) contains the true percent of American adults who do not think that human beings developed from earlier species.

(b) The poll used a method that provides an estimate within 3%of the truth about the population 95%of the time.

(c) If Harris takes another poll using the same method, the results of the second poll will lie between 51%and 57%.

(d) Harris should have surveyed more people so that the margin of error would be 0%instead of 3%.

(e) The poll used a method that would result in an interval that contains 54%in 95%of all possible samples of the same size from this population.

6. Beer and BAC Refer to Exercise 4. Computer output from the least-squares regression analysis on the beer and blood alcohol data is shown below.


The model for regression inference has three parameters:伪,尾and蟽Explain what each parameter represents in context. Then provide an estimate for each.

A city wants to conduct a poll of taxpayers to determine the level of support for constructing a new city-owned baseball stadium. Which of the following is the primary reason for using a large sample size in constructing a confidence interval to estimate the proportion of city taxpayers who would support such a project?

(a) To increase the confidence level

(b) To eliminate any confounding variables

(c) To reduce nonresponse bias

(d) To increase the precision of the estimate

(e) To reduce under coverage

Students in Mr. Handford鈥檚 class dropped a kickball beneath a motion detector. The detector recorded the height of the ball as it bounced up and down several times. Here are the heights of the ball at the highest point on the first five bounces:

Bounce numberHeight (feet)12.24021.62031.23540.95850.756

Here is the scatter plot of the data

(a) The following graphs show the results of two different transformations of the data. Would an exponential model or a power model provide a better description of the relationship between bounce number and height? Justify your answer.

(b) Minitab output from a linear regression analysis on the transformed data of log(height) versus bounce number is shown below. Give the equation of the least-squares regression line. Be sure to define any variables you use.

PredictorCoefSE CoefTPConstant0.453740.0138532.760.000Bounce-0.1171600.004176-28.060.000

S=0.0132043R-Sq=99.6%R-Sq(adj)=99.5%

(c) Use your model from part (b) to predict the highest point the ball reaches on its seventh bounce. Show your work.

(d) A residual plot for the linear regression in part (b) is shown below. Do you expect your prediction part (c) to be too high, too low, or just right? Justify your answer.

In the casting of metal parts, molten metal flows through a 鈥済ate鈥� into a die that shapes the part. The gate velocity (the speed at which metal is forced through the gate) plays a critical role in die casting. A firm that casts cylindrical aluminium pistons examined a random sample of 12pistons formed from the same alloy of metal. What is the relationship between the cylinder wall thickness (inches) and the gate velocity (feet per second) chosen by the skilled workers who do the casting? If there is a clear pattern, it can be used to direct new workers or to automate the process. A scatterplot of the data is shown below

A least-squares regression analysis was performed on the data. Some computer output and a residual plot are shown below. A Normal probability plot of the residuals (not shown) is roughly linear.

Do these data provide convincing evidence of a straight-line relationship between thickness and gate velocity in the population of pistons formed from this alloy of metal? Carry out an appropriate significance test at the 伪=0.05level.
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