Practice Math Statistics Problems and Master the Concepts

Use the one-standard-deviation x2 $x^{2}$ -test and the one-standard-deviation $x^{2}$ -interval procedure to conduct the required hypothesis test and obtain the specified confidence interval. s=3 and n=10.
a. $H_{0} : σ = 4, H_{3} : σ < 4, α = 0.05$ .
b. 90% confidence interval

nagasenaz 2021-05-14

When σ is unknown and the sample size is $n \geq 30$ , there are tow methods for computing confidence intervals for μμ. Method 1: Use the Student's t distribution with d.f. = n - 1. This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method. Method 2: When $n \geq 30$ , use the sample standard deviation s as an estimate for σσ, and then use the standard normal distribution. This method is based on the fact that for large samples, s is a fairly good approximation for σσ. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution. Consider a random sample of size n = 31, with sample mean x¯=45.2 and sample standard deviation s = 5.3. (c) Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal distribution?

he298c 2021-05-13

A boy is to sell lemonade to make some money to afford some holiday shopping. The capacity of the lemonade bucket is 1. At the start of each day, the amount of lemonade in the bucket is a random variable X, from which a random variable Y is sold during the day. The two random variables X and Y are jointly uniform.
Find and sketch the CDF and the pdf of Z which is the amount of lemonade remaining at the end of the day. Clearly indicate the range of Z

Kaycee Roche 2021-05-13

How can you use a two-way table to determine probabilities?

Ayaana Buck 2021-05-13

Let the continuous random variables X and Y have joint pdf

$f (x, y) = e^{- x - y}, 0$

a) $e^{- y}$

b) $e^{- x}$

c) $\frac{e^{y}}{e^{- x}}$

geduiwelh 2021-05-13

Here are the row and column totals for a two-way table with two rows and two columns: $\begin{array}{llr} a & b & 50 \\ c & d & 50 \\ 60 & 40 & 100 \end{array}$ Find two different sets of counts a, b, c, and d for the body of the table that give these same totals. This shows that the relationship between two variables cannot be obtained from the two individual distributions of the variables.

FizeauV 2021-05-13

Assume the sample is from a normally distributed population and construct the indicated confidence intervals for (a) the population variance $σ^{2}$ and (b) the population standard deviation σ. Interpret the results. The record high daily temperatures (in degrees Fahrenheit) of a random sample of 64 days of the year in Grand Junction, Colorado, have a sample standard deviation of 16.8∘F. Use a 98% level of confidence.

boitshupoO 2021-05-12

Let $X_{1}, X_{2}, . . ., X_{6}$ be an i.i.d. random sample where each $X_{i}$ is a continuous random variable with probability density function
$f (x) = e^{- (x - 0)}, x > 0$
Find the probability density function for $X_{6}$ .

Tolnaio 2021-05-11

Car Repaors An automobile lealesrship has found that for every 140 cars sold, 23 will be brought back to the dealer for major repairs. If the dealership sells 980 cars this year, approximately how many cars will be brought back for major repairs?

Maiclubk 2021-05-09

If you have a 99% confidence interval for $μ; μ$ ; based on a simple random sample, is it correct to say that in the long run, if you computed many, many confidence intervals using the prescribed method, about 99% of such intervals would contain $μ$ ;? Explain.

ruigE 2021-05-09

The two intervals (114.4, 115.6) and (114.1, 115.9) are confidence intervals (The same sample data was used to calculate both values) for $μ =$ true average resonance frequency (in hertz) for all tennis rackets of a certain type.
a. What is the value of the sample mean resonance frequency?
b. The confidence level for one of these intervals is 90% and for the other it is 99%. Which is which, and how can you tell?

Wribreeminsl 2021-05-08

How can you read and make a two-way table?

Annette Arroyo 2021-05-08

When σ is unknown and the sample is of size $n \geq 30$ , there are two methods for computing confidence intervals for μ. Method1:Method1: Use the Student's t distribution with d.f. = n - 1. Method2:Method2: When $n \geq 30$ , use the sample standard deviation s as an estimate for σ,σ, and then use the standard normal distribution. Consider a random sample of size n = 31, with sample mean x¯=45.2 and sample standard deviation s = 5.3. Compute 90%, 95%, and 99% confidence intervals for μμ using Method 2 with the standard normal distribution. Use s as an estimate for σσ. Round endpoints to two digits after the decimal.

Phoebe 2021-05-08

You are given the sample mean and the population standard deviation. Use this information to construct 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. From a random sample of 24 months from January 2006 through December 2016, the mean number of tornadoes per month in the United States was about 100. Assume the population standard deviation is 114.

Burhan Hopper 2021-05-08

The analysis of shafts for a compressor is summarized by conformance to specifications: roundnessconforms yes no surface finish yes 3455 conforms no 128
(a) If we know that a shaft conforms to roundness requirements, what is the probability that it conforms to surface finish requirements?
(b) If we know that a shaft does not conform to roundness requirements, what is the probability that it conforms to surface finish requirements?

Jaden Easton 2021-05-08

The two-way table summarizes data from an experiment comparing the effectiveness of three different diets (A, B, and C) on weight loss. Researchers randomly assigned 300 volunteer subjects to the three diets. The response variable was whether each subject lost weight over a 1-year period.

$Diet Lost weight? \begin{array}{lcccc} A & B & C & Total \\ Yes & 60 & 180 \\ No & 40 & 120 \\ Total & 90 & 100 & 110 & 300 \end{array}$

Suppose we randomly select one of the subjects from the experiment. Show that the events "Diet B" and "Lost weight" are independent.

Marvin Mccormick 2021-05-08

For the poll described in the Chapter problem, assume that the respondents had been asked for their political party affiliation, and the responses were coded as 0 (for Democrat), 1 (for Republican), 2 (for Independent), or 3 (for any other response). If we calculate the average (mean) of the numbers and get 0.95, how can that value be interpreted?

ruigE 2021-05-08

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 the marginal density of Y.

Brennan Flores 2021-05-05

Suppose the random variables X and Y have a pdf given by
f(x,y)=x+y on 0<x<1, 0<y<1
Find P(X>Y).

Wribreeminsl 2021-05-05

A missile system's two electronic components must cooperate for the system as a whole to succeed. Let X and Y represent the combined life of the two components in hours. The joint density of X and Y is
$f (x, y) = y e^{- y (1 + x)}, x, y > 0$
Give the marginal density functions for both random variables. Are the independent?

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