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Chapter 12: Q. AP4.26. (page 803)

Which of the following statements about the t distribution with degrees of freedom df is (are) true?

I. It is symmetric.

II. It has more variability than the t distribution with df+1degrees of freedom.

III. As df increases, the t distribution approaches the standard Normal distribution.

(a) I only (c) III only (e) I, II, and III

(b) II only (d) I and II

Short Answer

Expert verified

(e) I, II and III are true.

Step by step solution

01

Given information

we have been given that

tdistribution with degree of freedom df

02

Explanation

I:True, because all t-distributions are symmetric.

II:True, because as the degree of freedom decreases, the t-distribution becomes wider and thus the t-distribution has more variability (when it has a lower degrees of freedom).

III:True, because the larger the degree of freedom, the more closely the t-distribution resembles the standard Normal distribution.

Since, I,IIandIIIare all correct, the correct answer option is(e)I,IIandIII

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Most popular questions from this chapter

Some high school physics students dropped a ball and measured the distance fallen (in centimeters) at various times (in seconds) after its release. If you have studied physics, then you probably know that the theoretical relationship between the variables is distance =490(time)2. A scatterplot of the students’ data showed a clear curved pattern. Which of the following single transformations should linearize the relationship? I. time2II. distance2III. distance

(a) I only

(c) III only

(e) I and III only

(b) II only

(d) I and II only

An experimenter wishes to test whether or not two types of fish food (a standard fish food and a new product) work equally well at producing fish of equal weight after a two-month feeding program. The experimenter has two identical fish tanks (1 and 2) to put fish in and is considering how to assign 40fish, each of which has a numbered tag, to the tanks. The best way to do this would be to

(a) put all the odd-numbered fish in one tank, the even in the other, and give the standard food type to the odd-numbered ones.

(b) obtain pairs of fish whose weights are virtually equal at the start of the experiment and randomly assign one to Tank 1 and the other to Tank2, with the feed assigned at random to the tanks.

(c) proceed as in part (b), but put the heavier of the pair into Tank2.

(d) assign the fish at random to the two tanks and give the standard feed to Tank1.

(e) not proceed as in part (b) because using the initial weight in part (b) is a nonrandom process. Use the initial length of the fish instead.

A residual plot from the least-squares regression is shown below. Which of the following statements is supported by the graph

(a) The residual plot contains dramatic evidence that the standard deviation of the response about the population regression line increases as the average number of putts per round increases.

(b) The sum of the residuals is not 0. Obviously, there is a major error present.

(c) Using the regression line to predict a player’s total winnings from his average number of putts almost always results in errors of less than \(200,000.

(d) For two players, the regression line under predicts their total winnings by more than\)800,000.

(e) The residual plot reveals a strong positive correlation between average putts per round and prediction errors from the least-squares line for these players.

The previous Check Your Understanding (page 750) described some results from a study of body weights and backpack weights. Here, again, is the Minitab output from the least-squares regression analysis for these data.

2. Would a 99 % confidence interval for the slope β of the population regression line include 0? Justify your answer. (You don't need to do any calculations to answer this question.)

Which of the following is not one of the conditions that must be satisfied in order to perform inference about the slope of a least-squares regression line? (a) For each value of x, the population of y-values is Normally distributed.

(b) The standard deviation σof the population of y-values corresponding to a particular value of x is always the same, regardless of the specific value of x. (c) The sample size—that is, the number of paired observations (x, y)—exceeds 30.

(d) There exists a straight line y=α+βxsuch that, for each value of x, the mean μyof the corresponding population of y-values lies on that straight line.

(e) The data come from a random sample or a randomized experiment.
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