\(\displaystyle={3}-{1}\)

\(\displaystyle={2}\) Thus, the degrees of freedom for the groups term is 2.

Question

2021-02-07

asked 2021-01-19

a) The statistic \(X^{2}\), that is used to estimate the variance \(S^{2}\) of a random sample, has a Chi-squared distribution.

b) The sum of the squares of k independent standard normal random variables has a Chi-squared distribution with k degrees of freedom.

c) The Chi-squared distribution is used in hypothesis testing and estimation.

d) The Chi-squared distribution is a particular case of the Gamma distribution.

e)All of the above.

asked 2021-01-25

asked 2020-12-30

The tables show the battery lives (in hours) of two brands of laptops.
a) Make a double box-and-whisker plot that represent's the data.
b) Identifity the shape of each distribution.
c) Which brand's battery lives are more spread out? Explain.
d) Compare the distributions using their shapes and appropriate measures of center and variation.

asked 2021-03-07

\(\begin{array}{|c|c|} \hline Subject & (1) & (2) & (3) & (4) & (5) &(6) & (7) & (8) & (9) \\ \hline Black & 25.85 & 28.84 & 32.05 & 25.74 & 20.89 & 41.05 & 25.01 & 24.96 & 27.47 \\ \hline White & 18.28 & 20.84 & 22.96 & 19.68 & 19.509 & 24.98 & 16.61 & 16.07 & 24.59 \\ \hline \end{array}\)

Does the data indicate that the higher level of illumination yields a decrease of more than 5 sec in true average task completion time? Test the appropriate hypotheses using the P-value approach.

asked 2020-11-26

An analysis of laboratory data collected with the goal of modeling the weight (in grams) of a bacterial culture after several hours of growth produced the least squares regression line \(\log(weight) = 0.25 + 0.61\)hours. Estimate the weight of the culture after 3 hours.

A) 0.32 g

B) 2.08 g

C) 8.0 g

D) 67.9 g

E) 120.2 g

asked 2020-11-07

1)A rewiew of voted registration record in a small town yielded the dollowing data of the number of males and females registered as Democrat, Republican, or some other affilation:

\(\begin{array}{c} Gender \\ \hline Affilation & Male & Female \\ \hline Democrat & 300 & 600 \\ Republican & 500 & 300 \\ Other & 200 & 100 \\ \hline \end{array}\)

What proportion of all voters is male and registered as a Democrat? 2)A survey was conducted invocted involving 303 subject concerning their preferences with respect to the size of car thay would consider purchasing. The following table shows the count of the responses by gender of the respondents:

\(\begin{array}{c} Size\ of\ Car \\ \hline Gender & Small & Medium & lange & Total \\ \hline Female & 58 & 63 & 17 & 138 \\ Male & 79 & 61 & 25 & 165 \\ Total & 137 & 124 & 42 & 303 \\ \hline \end{array}\)

the data are to be summarized by constructing marginal distributions. In the marginal distributio for car size, the entry for mediums car is ?

asked 2020-12-28

asked 2020-10-23

A random sample of \(\displaystyle{n}_{{1}}={16}\) communities in western Kansas gave the following information for people under 25 years of age.

\(\displaystyle{X}_{{1}}:\) Rate of hay fever per 1000 population for people under 25

\(\begin{array}{|c|c|} \hline 97 & 91 & 121 & 129 & 94 & 123 & 112 &93\\ \hline 125 & 95 & 125 & 117 & 97 & 122 & 127 & 88 \\ \hline \end{array}\)

A random sample of \(\displaystyle{n}_{{2}}={14}\) regions in western Kansas gave the following information for people over 50 years old.

\(\displaystyle{X}_{{2}}:\) Rate of hay fever per 1000 population for people over 50

\(\begin{array}{|c|c|} \hline 94 & 109 & 99 & 95 & 113 & 88 & 110\\ \hline 79 & 115 & 100 & 89 & 114 & 85 & 96\\ \hline \end{array}\)

(i) Use a calculator to calculate \(\displaystyle\overline{{x}}_{{1}},{s}_{{1}},\overline{{x}}_{{2}},{\quad\text{and}\quad}{s}_{{2}}.\) (Round your answers to two decimal places.)

(ii) Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use \(\displaystyle\alpha={0.05}.\)

(a) What is the level of significance?

State the null and alternate hypotheses.

\(\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}},{H}_{{1}}:\mu_{{1}}<\mu_{{2}}\)

\(\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}},{H}_{{1}}:\mu_{{1}}>\mu_{{2}}\)

\(\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}},{H}_{{1}}:\mu_{{1}}\ne\mu_{{2}}\)

\(\displaystyle{H}_{{0}}:\mu_{{1}}>\mu_{{2}},{H}_{{1}}:\mu_{{1}}=\mu_{{12}}\)

(b) What sampling distribution will you use? What assumptions are you making?

The standard normal. We assume that both population distributions are approximately normal with known standard deviations.

The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations,

The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations,

The Student's t. We assume that both population distributions are approximately normal with known standard deviations,

What is the value of the sample test statistic? (Test the difference \(\displaystyle\mu_{{1}}-\mu_{{2}}\). Round your answer to three decimalplaces.)

What is the value of the sample test statistic? (Test the difference \(\displaystyle\mu_{{1}}-\mu_{{2}}\). Round your answer to three decimal places.)

(c) Find (or estimate) the P-value.

P-value \(\displaystyle>{0.250}\)

\(\displaystyle{0.125}<{P}-\text{value}<{0},{250}\)

\(\displaystyle{0},{050}<{P}-\text{value}<{0},{125}\)

\(\displaystyle{0},{025}<{P}-\text{value}<{0},{050}\)

\(\displaystyle{0},{005}<{P}-\text{value}<{0},{025}\)

P-value \(\displaystyle<{0.005}\)

Sketch the sampling distribution and show the area corresponding to the P-value.

P.vaiue Pevgiue

P-value f P-value

asked 2020-11-07

asked 2021-01-25

\(\begin{array}{|c|c|}\hline \text{Year} & \text{Average tuition} \\ \hline 2005 & $17.6 \\ \hline 2007 & $18.1 \\ \hline 2009 & $19.5 \\ \hline 2011 & $20.7 \\ \hline 2013 & $21.8 \\ \hline \end{array}\)

What prediction does the formula modeling this data give for average yearly tuition and required fees for the university for the academic year beginning in 2019?