Practice Math Statistics Problems and Master the Concepts

A certain reported that in a survey of 2006 American adults, $24 %$ said they believed in astrology.
a) Calculate a confidence interval at the $99 %$ confidence level for the proportion of all adult Americans who believe in astrology. (Answers should be rounded to three decimal places.)
(_, _)
b) What sample size would be required for the width of a $99 %$ CI to be at most 0.05 irresoective of the value of $\hat{p}$ ? (Round your answer up to the nearest integer.)

babeeb0oL 2021-08-06

You are concerned about the effects of texting on driving performance. Design a study to test the response time of drivers while texting and while driving only. How many seconds does it take for a driver to respond when a leading car hits the brakes? a. Describe the explanatory and response variables in the study. b. What are the treatments? c. What should you consider when selecting participants? d. Your research partner wants to divide participants randomly into two groups: one to drive without distraction and one to text and drive simultaneously. Is this a good idea? Why or why not? e. Identify any lurking variables that could interfere with this study. f. How can blinding be used in this study?

OlmekinjP 2021-08-06

An alternative to the lognormal distribution for modeling highly skewed populations is the Pareto distribution with parameters θ and r. The probability density function is

Rivka Thorpe 2021-08-06

What are the data modeling concepts used in MongoDB? What are the main CRUD operations of MongoDB?

Ava-May Nelson 2021-08-06

What are the data modeling concepts used in column-based NOSQL systems and Hbase?

UkusakazaL 2021-08-06

It was observed that 30 of the 100 randomly selected students smoked. Find the confidence interval estimate of $95 %$ confidence level for $π$ ratio of smokers in the population.
a) $P (0.45 < p < 0.78) = 0.95$
b) $P (0.11 < p < 0.28) = 0.95$
c) $P (0.51 < p < 0.78) = 0.95$
d) $P (0.21 < p < 0.59) = 0.95$
e) $P (0.21 < p < 0.39) = 0.95$

UkusakazaL 2021-08-06

The probability density function of X is $f (x) = \frac{1}{10}$ for $0 \leq x \leq 10$ . Then $P (X + \frac{10}{X} \geq 7)$ is:

UkusakazaL 2021-08-06

In a sample of 7 cars, each car was tested for nitrogen-oxide emissions and the following results were obtained: 0.06, 0.11, 0.16, 0.15, 0.14, 0.08, 0.15. Assuming that the sample is representative of all cars in use and that they are normally distributed, construct a $98 %$ confidence interval estimate for the mean amount of nitrogen-oxide emission for all cars.
Use the sample data from #4 to construct a $98 %$ confidence interval estimate for the standard deviation of the amount nitrogen-oxide emission for all cars.

UkusakazaL 2021-08-06

Assume that $σ$ is unknown, the lower $100 (1 - α) %$ confidence bound on $μ$ is:
a) $μ \leq \overset{―}{x} + t_{α, n - 1} \frac{s}{\sqrt{n}}$
b) $\overset{―}{x} - t_{α, n - 1} \frac{s}{\sqrt{n}} \leq μ$
c) $μ \leq \overset{―}{x} + t_{\frac{α}{2}, n - 1} \frac{s}{\sqrt{n}}$
d) $\overset{―}{x} - t_{\frac{α}{2}, n - 1} \frac{s}{\sqrt{n}} \leq μ$

UkusakazaL 2021-08-05

Probability of accept a hypothesis when it is wrong is known as _______
a. Type II error
b. Significance level
c. Confidence level
d. Type I error

UkusakazaL 2021-08-05

Find the critical value $z_{\frac{α}{2}}$ that corresponds to the given confidence level.
$96 %$

UkusakazaL 2021-08-05

$\begin{array}{cc} 25.6 & 23.8 & 26.5 & 23.9 & 24.8 \\ 24.7 & 20.9 & 26 & 22.2 & 27 \end{array}$
What Equation to use to construct a $99 %$ lower confidence bound for $σ^{2}$

UkusakazaL 2021-08-05

Data such as "occupation" would use categorical frequency distributions:
True and False?

UkusakazaL 2021-08-05

Five people have a genetic disease and one child each. The random variable x is the number of children among the five who inherit the disease.
a)Find the mean.
b)Find the standard deviation.
$\begin{array}{cc} x & 0 & 1 & 2 & 3 & 4 & 5 \\ P (x) & 0.027 & 0.162 & 0.311 & 0.311 & 0.162 & 0.027 \end{array}$

UkusakazaL 2021-08-05

Find the value: $t_{\frac{a}{2}}$ if $n = 18$ for the $99 %$ confidence interval for the mean.

UkusakazaL 2021-08-04

The average annual mileage of a car is 23,500 kilometers, with a standard deviation of 3900 kilometers, according to a sample of 100 Virginians who own cars.
Assume that the measurement distribution is roughly normal.
a) Create a 99 percent confidence interval for the typical Virginian vehicle's annual mileage in kilometers.
b) If we assume that Virginians drive an average of 23,500 kilometers per year, what can we say with 99 percent certainty about the potential extent of our error?

slaggingV 2021-08-04

Calculate the amount that follows the given investment. $$ 700$ invested at $4 %$ compounded daily after a period of 4 years:
After 4 years, the investement results in how much $?

UkusakazaL 2021-08-04

a. Let $X \sim N (0, 1) and E \sim N (0, 1)$ be independent, and let $Y = X + β E$ . Show that $r_{x y} = \frac{1}{\sqrt{β^{2} + 1}}$ b.Use the results of part (a) to generate bivariate samples (x_i, y_i) of size 20 with population correlation coefficients −.9, −.5, 0, .5, and .9, and compute the sample correlation coefficients. c. Have a partner generate scatterplots as in part (b) and then guess the correlation coefficients.

emancipezN 2021-08-04

Let x be a binomial random variable with $n = 20$ and $p = \frac{42}{100} .$
a) Calculate the mean, variance and standard deviation of the random variable x.
b) Use the results of part a to calculate the intervals $μ \pm σ, μ \pm 2 σ,$ and $μ \pm 3 σ$ . Find the probability that an observation will fall into each of these intervals.
c) Are the results of part b consistent with Tchebysheff’s Theorem? With the Empirical Rule? Why or why not?

abondantQ 2021-08-04

On a certain day, a large number of fuses were manufactured, each rated at 15 A. A sample of 75 fuses is drawn from the day’s production, and 17 of them were found to have burnout amperages greater than 15 A.
a) Find a $95 %$ confidence interval for the proportion of fuses manufactured that day whose burnout amperage is greater than 15 A.
b) Find a $98 %$ confidence interval for the proportion of fuses manufactured that day whose burnout amperage is greater than 15 A.
c) Find the sample size needed for a $95 %$ confidence interval to specify the proportion to within $\pm 0.05 .$

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