College statistics and probability problems, solved and explained

Recent questions in Statistics and Probability

permaneceerc 2020-10-20

The probability distribution used when making inferences about a single population variance is ?
The probability distribution used when comparing two population variance is ?
The F test for comparing two population variances is known to be sensitive to the assumption of ?

Khaleesi Herbert 2020-10-20

Do the following summarize a categorical variable or a numerical variable? Explain.
(a) For a football player, the shooting percentage during one game
(c) For a baseball player, his batting average during the playoffs
(d) For a hockey player, the time on ice per game

Carol Gates 2020-10-20

A January 2007 Gallup Poll question asked, "In general, do you think things have gotten better or gotten worse in this country in the last five years?" Possible answers were “Better”, "Worse”, "No Change", “Don't Know”, and “No Response". What kind of variable is the response?

UkusakazaL 2020-10-20

The table shows the total cost c of buying t movie tickets. Write an equation to represent the relationship between c and t.

$\begin{array}{cc} t & с \\ 1 & 7 \\ 2 & 14 \\ 3 & 21 \\ 4 & 28 \end{array}$

Line 2020-10-20

Suppose you are testing whether the lifetime of 4 different types of lightbulbs. You run 5 experiments each. You get a mean square error of $M S_{E} = 1.75$ and you reject the null hypothesis. The sample means you obtain for each lightbulb are below:
Type 1: 20
Type 2: 30
Type 3: 28
Type 4: 22
Which pairs are significantly different at the $5 %$ significance level? Select all that apply.

waigaK 2020-10-20

A population of values has a normal distribution with $μ = 26.8$ and $σ = 33.8$ . You intend to draw a random sample of size $n = 89$ .
Find the probability that a single randomly selected value is between 17.1 and 25.
$P (17.1 < X < 25) =$ ?
Write your answers as numbers accurate to 4 decimal places.

slaggingV 2020-10-20

A) Explain why the chi-square goodness-of-fit test is not an appropriate way to find out.
B) What might you do instead of weighing the nuts in order to use a x2 test?
Nuts A company says its premium mixture of nuts con- tains 10% Brazil nuts, 20% cashews, 20% almonds, and 10% hazelnuts, and the rest are peanuts. You buy a large can and separate the various kinds of nuts. Upon weigh- ing them, you find there are 112 grams of Brazil nuts, 183 grams of cashews, 207 grams of almonds, 71 grams of hazelnuts, and 446 grams of peanuts. You wonder whether your mix is significantly different from what the company advertises.

Tammy Todd 2020-10-19

Researchers carried out a survey of fourth-, fifth-, and sixth-grade students in Michigan. Students were asked whether good grades, athletic ability, or being popular was most important to them. This two-way table summarizes the survey data.

$\begin{matrix} G r a d e M o s t i m p o r t a n t & \begin{array}{lcccc} \begin{matrix} 4 th g r a d e \end{matrix} & \begin{matrix} 5 th grade \end{matrix} & \begin{matrix} 6 th g r a d e \end{matrix} & T o t a l \\ G r a d e s & 49 & 50 & 69 & 168 \\ A t h l e t i c & 24 & 36 & 38 & 98 \\ P o p u l a r & 19 & 22 & 28 & 69 \\ T o t a l & 92 & 108 & 135 & 335 \end{array} \end{matrix}$

Suppose we select one of these students at random. What's the probability that: The student is a sixth grader or a student who rated good grades as important?

FizeauV 2020-10-19

In an experiment designed to study the effects of illumination level on task performance (“Performance of Complex Tasks Under Different Levels of Illumination,” J. Illuminating Eng., 1976: 235–242), subjects were required to insert a fine-tipped probe into the eyeholes of ten needles in rapid succession both for a low light level with a black background and a higher level with a white background. Each data value is the time (sec) required to complete the task.
$\begin{array}{cc} S u b j e c t & (1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) & (9) \\ B l a c k & 25.85 & 28.84 & 32.05 & 25.74 & 20.89 & 41.05 & 25.01 & 24.96 & 27.47 \\ W h i t e & 18.28 & 20.84 & 22.96 & 19.68 & 19.509 & 24.98 & 16.61 & 16.07 & 24.59 \end{array}$
Does the data indicate that the higher level of illumination yields a decrease of more than 5 sec in true average task completion time? Test the appropriate hypotheses using the P-value approach.

ringearV 2020-10-19

A chi-square homogeneity test is to be conducted to decide whether four populations are nonhomogeneous with respect to a variable that has eight possible values. What are the degrees of freedom for the $x^{2}$ -statistic?

CheemnCatelvew 2020-10-18

A population of values has a normal distribution with $μ = 239.5$ and $σ = 32.7$ . You intend to draw a random sample of size $n = 139$ .
Find the probability that a single randomly selected value is greater than 235.9.
$P (X > 235.9) =$ ?
Write your answers as numbers accurate to 4 decimal places.

waigaK 2020-10-18

Consider the following function. $f (x) = \frac{x^{2}}{x^{2} - 81}$ a) To find the critucal numbers of f. b) To find the open interval on which function is increasing or decreasing. c) To identify the relative extremum.

Yasmin 2020-10-18

In statistics, random samples are used to make generalizations, or inferences, about a population. Give a full correct answer for this question its true or false?

beljuA 2020-10-18

Give full and correct answer for this question, the chi-square test can be used: Select one: a. to make inference about a population mean. b. to test for survey error. c. to compare more than two independent proportions. d. for pairwise multiple comparisons of means. e. to test for difference in two variances.

zi2lalZ 2020-10-18

Suppose a product costs R10 and the profit rate is 20% on the cost price, find the selling price

illusiia 2020-10-18

A February 2007 Gallup Poll question asked, “In politics, as of today, do you consider yourself a Republican, a Democrat, or an Independent?” The possible responses were "Democrat". "Republican". “Independent”, “Other”, and “No Response”. What kind of variable to the response?

ossidianaZ 2020-10-18

How to solve this confidence interval? Use the confidence interval to find the estimated margin of error. Then find the sample mean. A store manager says a confidence interval of (44.07, 80.97) when estimating the mean price (in dollars) for the population of textbooks.

lwfrgin 2020-10-18

How is the distinction between qualitative and quantitative data in social research is essentially the distinction between numerical and nonnumerical data?

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