Practice Math Statistics Problems and Master the Concepts

Use the one-standard-deviation $x^{2}$ -test and the one-standard-deviation $x^{2}$ -interval procedure to conduct the required hypothesis test and obtain the specified confidence interval. $s = 5$ and $n = 20$
a. $H_{0} : σ = 6, H_{a} : σ \neq 6, α = 0.05$ .
b. 95% confidence interval

Brennan Flores 2021-05-21

When comparing two sets of data values, what is the advantage of using relative frequency distributions instead of frequency distributions?

Jaden Easton 2021-05-21

Use the summation formulas to rewrite the expression without the summation notation. Use the result to find the sums for n= 10, 100, 1000, and 10,000. $\sum_{i = 1}^{n} \frac{2 i + 1}{n^{2}}$

Josalynn 2021-05-21

Consider a normal population distribution with the value of $σ$ known?
a. What is the confidence level for the interval $\overset{―}{X} \pm 2.81 \frac{σ}{\sqrt{n}} ?$
b. What is the confidence level for the interval $\overset{―}{X} \pm 1.44 \frac{σ}{\sqrt{n}} ?$

necessaryh 2021-05-19

Construct two 99% confidence intervals for $μ_{X} = μ_{Y}$ using the data of Case Study 9.2.3, first assuming the variances are equal, and then assuming they are not.

shadsiei 2021-05-19

Random variables $X_{1}, X_{2}, . . ., X_{n}$ are independent and identically distributed. 0 is a parameter of their distribution.
State the definition for a pivotal function of X, the vector of random variables, and 0.

Carol Gates 2021-05-19

Use the row of numbers shown below to generate 12 random numbers between 01 and 99.
78038 18022 84755 23146 12720 70910 49732 79606
Starting at the beginning of the row, what are the first 12 numbers between 01 and 99 in the sample?

Ernstfalld 2021-05-18

Find the expected values and variances of the exponential random variables with the density functions given below
$3 e^{- 3 x}$

e1s2kat26 2021-05-18

Solve by using the strategy Work Backward. A beetle needs to climb out of a crater that is 800 cm deep. It advances 120 cm each day, but is slips back 90 cm while resting each night. How many days will it take before this beetle successfully climbs out of the crater?

Nann 2021-05-18

In a study designed to determine whether babies have an innate sense of morality, babies were shown two puppet shows in a random order: one of them had a puppet being nice, and the other had a different puppet being mean. The babies were then given the opportunity to reach for either the nice puppet or the mean puppet, and the researchers recorded which puppet the babies reached for. Suppose that out of 23 babies in the study, 15 of them reached for the nice puppet. Using the distribution you picked and observed 15 out of 23 babies reaching for the nice puppet, what conclusion should be drawn, and why?

Haven 2021-05-18

Random variables Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: X-20

banganX 2021-05-18

Two random variables X and Y with joint density function given by:
$f (x, y) = {\begin{cases} \frac{1}{3} (2 x + 4 y) & 0 \leq x, \leq 1 \\ 0 & e l s e w h e r e \end{cases}$
Find $P (x < \frac{1}{3})$

Cabiolab 2021-05-17

The yield strength of CP titanium welds was measured for welds cooled at rates of $10^{\circ} C; s, 15^{\circ} C; s, and 28^{\circ} C; s$ . The results are presented in the following table. (Based on the article “Advances in Oxygen Equivalence Equations for Predicting the Properties of Titanium Welds,” D. Harwig, W. Ittiwattana, and H. Castner, The Welding Journal, 2001:126s-136s.)

$\begin{matrix} Cooling Rate & Yiled Strengths \\ 10 & 71.00 & 75.00 & 79.67 & 81.00 & 75.50 & 72.50 & 73.50 & 78.50 & 78.50 \\ 15 & 63.00 & 68.00 & 73.00 & 76.00 & 79.67 & 81.00 \\ 28 & 68.65 & 73.70 & 78.40 & 84.40 & 91.20 & 87.15 & 77.20 & 80.70 & 84.85 & 88.40 \end{matrix}$
a. Construct an ANOVA table. You may give a range for the P-value. b. Can you conclude that the yield strength of CP titanium welds varies with the cooling rate?

Ernstfalld 2021-05-17

Suppose the random variables X and Y have a pdf given by
f(x,y)=x+y on 0 Find F( $\frac{1}{4}, \frac{1}{2}) .$

Reeves 2021-05-16

Carol and Alina play soccer for a local college team. Based on anecdotal evidence, they think that there is a difference in a player success rate of taking penalty kicks with their dominant foot compared to their non-dominant foot. They would like to test this hypothesis with an experiment. Carol arranges for each of the 11 starting players on her team to take ten penalty kicks with their dominant foot and ten penalty kicks with their non dominant foot and records the data. Using the same data values, describe two distributions that would be more supportive of the hypothesis.

Mylo O'Moore 2021-05-16

X and Y are independent rv's with moment generating functions $M_{X} (t)$ and $M_{Y} (t)$ , respectively. If Z=X+Y, we need to show that $M_{Z} (t) = M_{X} (t) M_{Y} (t)$ .

e1s2kat26 2021-05-16

Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma. Over a period of months, an adult male patient has taken eight blood tests for uric acid. The mean concentration was $x = 5.35 m \frac{g}{d l}$ . The distribution of uric acid in healthy adult males can be assumed to be normal with $σ = 1.85 m \frac{g}{d l} σ = 1.85 m \frac{g}{d l}$ . What conditions are necessary for your calculations?

Wotzdorfg 2021-05-16

Construct the indicated confidence intervals for (a) the population variance $σ^{2}$ and (b) the population standard deviation $σ$ . Assume the sample is from a normally distributed population. c = 0.90, s = 35, n = 18

allhvasstH 2021-05-16

Let $X_{1} . . . ., X_{n} a n d Y_{1}, . . ., Y_{m}$ be two sets of random variables. Let $a_{i}, b_{j}$ be arbitrary constant.
Show that
$C o v (\sum_{i = 1}^{n} a_{i} X_{i}, \sum_{j = 1}^{m} b_{j} Y_{j}) = \sum_{i = 1}^{n} \sum_{j = 1}^{m} a_{i} b_{j} C o v (X_{i}, Y_{j})$

tinfoQ 2021-05-14

Which graph used in a residual analysis provides roughly the same information as a scatterplot? What advantages does it have over a scatterplot?

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