Practice Math Statistics Problems and Master the Concepts

Suppose that $Y_{1}, Y_{2}, Y_{3}$ denote a random sample from anexponential distribution with density function $f (y) = (\frac{1}{λ}) \cdot e^{\frac{- y}{θ}}, y > 0$
=0 elsewhere
Consider the following five estimators of $θ$ :
${\hat{θ}}_{1} = Y_{1}, {\hat{θ}}_{2} = \frac{Y_{1} + Y_{2}}{2}, {\hat{θ}}_{3} = \frac{Y_{1} + 2 Y_{2}}{3}, {\hat{θ}}_{4} = \overset{―}{Y}$
a) Which of these estimators are unbiased?
b) Among the unbiased estimators, which has the smallest variance?

Wierzycaz 2021-02-02

Check Requirements What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?

waigaK 2021-02-02

Solve the general initial value problem modeling the LR circuit, $L \frac{d I}{d t} + R I = e, I (0) = I_{0}$ where E is a constant source of emf.

midtlinjeg 2021-02-02

Determine which of the following functions $f (x) = c x, g (x) = c x^{2}, h (x) = c \sqrt{| x |}, and r (x) = \frac{c}{x}$ can be used to model the data and determine the value of the constant c that will make the function fit the data in the table. $\begin{array}{cc} x & - 4 & - 1 & 0 & 1 & 4 \\ y & - 32 & - 2 & 0 & - 2 & - 32 \end{array}$

Bergen 2021-02-02

The measure of the supplement of an angle is $40^{\circ}$ more than three times the measure of the original angle. Find the measure of the angles. Instructions: Use the statement: " Let the original angle be x " to begin modeling the working of this question.

a) Write algebraic expression in terms of x for the following:

I) $40^{\circ}$ more than three times the measure of the original angle

II) The measure of the Supplement angle in terms of the original angle, x

b) Write an algebraic equation in x equating I) and II) in a)

c) Hence solve the algebraic equation in

b) and find the measure of the angles.

FizeauV 2021-02-02

A population of values has a normal distribution with $μ = 13.2$ and $σ = 5$ . You intend to draw a random sample of size $n = 60$ .
Find the probability that a single randomly selected value is between 11.5 and 14.
$P (11.5 < X < 14) =$ ?
Write your answers as numbers accurate to 4 decimal places.

babeeb0oL 2021-02-02

Potential buyers for a new car were randomly divided into two groups. One group was shown the "A" version of an ad for the car, while the other group was shown the "B" version of the ad. All were then tested on their recall of key points made in the ad. The researcher should run a hypothesis test based upon a comparison of means for ?
In another study, a healthcare insurance company took measures of subscribers’ cardiac (heart) health. The people were then provided an app for their phones which provided "nudges" and reminders about heart-healthy behaviors, such as eating more vegetables and less fried or fatty food, taking walks and breaks from sitting too long, and getting enough sleep. After 4 months of having the app, the cardiac health measures were taken again, with the objective of seeing if nudges from the app would result in decreased cardiac risk. The researcher should run a hypothesis test based on a comparison of means for?

Bergen 2021-02-02

The Pew Research Center polled a random sample of 2024 American adult cellphone owners to find out their age and if they own an iPhone, an Android, or something else (including non-smartphones). The data are summarized in the two-way table.
$\begin{array}{ccccc} 18 - 34 & 35 - 54 & 55 + & Total \\ iPhone & 169 & 171 & 127 & 467 \\ Androod & 214 & 189 & 100 & 503 \\ Other & 134 & 277 & 643 & 1054 \\ Total & 517 & 637 & 870 & 2024 \end{array}$
Let's say we choose one of the survey participants at random. What is the chance that the person is not between the ages of 18 and 34 and doesn't have an iPhone?

sanuluy 2021-02-01

As a vaccine scientist, you are required to test your newly developed vaccine in two different populations, populations Xand Y to ensure the safety and effectiveness of the vaccine. There are 3190 subjects from database X and 6094 subjects from database Therefore, you must select a number of subjects from populations X and Y to form a group. The newly formed of group must consist of subjects from both populations without repetition. The maximum number of groups which can be formed is denoted as d.
(1) Use Euclidean algorithm to find $d = G C D (X, Y) .$
2) Find the integers s and tsuch that $d = s X + t Y$
3) With the answer obtained from a, what is the ratio of subjects selected from population $X a n d Y, P X : P Y .$
4) Find Least Common Multiple for $X a n d Y, L C M (X, Y) .$

kuCAu 2021-02-01

Give a full and correct answer what is inference concerning the ration of two populations?

he298c 2021-02-01

What is the correlation coefficient and what is its significance? Explain why correlation coefficient is bound between -1 and 1. How correlation coefficient depicts itself in scatterplots? Aside from probabilistic models, explain what is least squares line fitting.

remolatg 2021-02-01

To explain:Why the test for homogeneity follows the same procedures as the test for independence.

Jaya Legge 2021-02-01

Suppose $f (x) = 2 x^{3} .$ Write an expression in terms of x and h that represents the average rate of change of f over any interval of length h. [That is, over any interval (x, x + h)] Simplify your answer as much as possible.

ka1leE 2021-01-31

Critical Thinking Let x be a random variable representing the amount of sleep each adult in New York City got last night. Consider a sampling distribution of sample means $\overset{―}{x}$ .
What value will the standard deviation $σ_{\overset{―}{x}}$ of the sampling distribution approach?

mattgondek4 2021-01-31

In a study, the data you collect is Gender
What type of the data is this?
Quantitative - Discrete
Quantitative - Continuous
Qualitative (Categorical)

FobelloE 2021-01-31

In Exercises, state whether the investigation in question is an observational study or a designed experiment. Justify your answer in each case.
Starting Salaries. The National Association of Colleges and Employers (NACE) compiles information on salary offers to new college graduates and publishes the results in Salary Survey.

nitraiddQ 2021-01-31

Describe the spread in running times based on quartiles.
The data represents the average drive (in yards) for 186 professional golfers on the men’s PGA tour in 2011. The first quartile is 285.2 yards and third quartile is 297.5 yards.

glasskerfu 2021-01-31

Forecasting
Forecasting is important relative to capacity requirements planning.
What are some of the merits of using judgment methods (i.e., qualitative data) in contrast to quantitative forecasting methods.
Which methods are considered to be superior or more accurate, and in what forecast situations would require judgment methods?
In what situations would require a quantitative approach to forecasting?

Alyce Wilkinson 2021-01-31

To describe:How would you test the representative's claim and also identify the type of the test.

lwfrgin 2021-01-31

To explain:Whether the given statement is correct or not

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