Practice Math Statistics Problems and Master the Concepts

Random variables X and Y have joint PDF
$f_{X, Y} (x, y) = {\begin{cases} 12 e^{- (3 x + 4 y)}, x \geq 0, y \geq 0 \\ 0, o t h e r w i s e \end{cases}$
Find $P [m i n (X, Y) \geq 2]$

Wierzycaz 2021-05-28

If X and Y have the same independent distributions with mean $μ$ and variance $σ^{2}$ , find $E [(X - Y)^{2}]$

Brennan Flores 2021-05-28

Find the margin of error for the given values of c,s, and n. c=0.95, s=2.2, n=64

aflacatn 2021-05-28

Represent sampling distributions in the format of a table that lists the different values of the sample statistic along with their corresponding probabilities. Given that the data consist of ranks, does it really make sense to identify the sampling distribution of the sample means?

foass77W 2021-05-27

Random variables Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: 0.5Y

Falak Kinney 2021-05-27

Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test.
$H_{0} : P = 0.52$ versus $H_{1} : p < 0.52$
$N = 150, X = 72, α = 0.1$
Is $N P_{0} (1 - P_{0})$ greater than or equal to 10?
Use technology to find the P-Value.

Alyce Wilkinson 2021-05-27

You randomly survey students in your school about whether they liked a recent school play. The two-way table shows the results. Find and interpret the marginal frequencies.

$\begin{array}{cc} Student \\ Liked & Did Not like \\ Gender & Male & 48 & 12 \\ Female & 56 & 14 \end{array}$

Dolly Robinson 2021-05-26

You are given the sample mean and the population standard deviation. Create 90% and 95% confidence intervals for the population mean using this information. Interpret the results and compare the widths of the confidence intervals. From a random sample of 36 business days from February 24, 2016, through February 24, 2017, the mean closing price of Apple stock was $116.16. Assume the standard deviation for the population is $10.27.

Dottie Parra 2021-05-26

Construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals. In a survey of 2241 U.S. adults in a recent year, 1322 say they have made a New Year's resolution.

a2linetagadaW 2021-05-26

Random variables $X_{1}, X_{2}, . . ., X_{n}$ are independent and identically distributed. 0 is a parameter of their distribution.
If $X_{1}, X_{2}, . . ., X_{n}$ are Normally distributed with unknown mean 0 and standard deviation 1, then $\overset{―}{X} \sim N (\frac{0, 1}{n})$ . Use this result to obtain a pivotal function of X and 0.

emancipezN 2021-05-26

If 95% Tukey confidence intervals tell us to reject $H_{0} : μ_{1} = μ_{2}$ and $H_{0} : μ_{1} = μ_{3}$ , will we necessarily reject $H_{0} : μ_{2} = μ_{3} ?$

Carol Gates 2021-05-26

The two-way table below describes the members of the U.S Senate in a recent year.
Male Female
Democrats 47 13
Republicans 36 4
If we select a U.S. senator at random, what's the probability that the senator is a female or a Democrat?

Kye 2021-05-25

Suppose that an i.i.d. sample of size 15 from a normal distribution gives X¯=10 and $s^{2}$ =25. Find 90% confidence intervals for μ and $σ^{2}$ .

jernplate8 2021-05-25

Using the health records of ever student at a high school, the school nurse created a scatterplot relating y = height (in centimeters) to x = age (in years). After verifying that the conditions for the regression model were met, the nurse calculated the equation of the population regression line to be & $μ; 0 = 105 + 4.2 x$ with & $σ; = 7$ cm. According to the population regression line, what is the average height of 15-year-old students at this high school?

Braxton Pugh 2021-05-25

The means of the number of revolutions per minute of two competing engines are to be compared. Thirty engines are randomly assigned to be tested. Both populations have normal distributions. Table 10.9 shows the result. Do the data indicate that Engine 2 has higher RPM than Engine 1? Test at a 5% level of significance. EngineSample Mean Number of RPMPopulation Standard Deviation 11,50050 21,60060 Table 10.9

Kyran Hudson 2021-05-25

The area enclosed by the x and y axes has a uniform distribution of the random variables X and Y, and the curve $y = 1 - x^{2}$ .
Compute E. (XY)

opatovaL 2021-05-23

Random variables $X_{1}, X_{2}, . . ., X_{n}$ are independent and identically distributed. 0 is a parameter of their distribution.
If $q (X, 0) \sim N (0, 1)$ is a pivotal function for 0, explain how you would use this result to obtain a symmetrical 95% confidence interval for 0.

nagasenaz 2021-05-23

Suppose that X and Y are continuous random variables with joint pdf $f (x, y) = e^{- (x + y)} 0$ and zero otherwise.
Find $P (X > 3)$

Bevan Mcdonald 2021-05-23

Compute the distribution of X+Y in the following cases:
X and Y are independent binomial random variables with parameters (n,p) and (m,p).

aortiH 2021-05-22

A random sample of 1200 U.S. college students was asked, "What is your perception of your own body? Do you feel that you are overweight, underweight, or about right?" The two-way table summarizes the data on perceived body image by gender. $\begin{array}{ccc} Gender \\ Body image & \begin{array}{lccr} Female & Male & Total \\ About right & 560 & 295 & 855 \\ Overwerght & 163 & 72 & 235 \\ Underweight & 37 & 73 & 110 \\ Total & 760 & 440 & 1200 \end{array} \end{array}$ What percent of respondents are males and feel that they are overweight or underweight?

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