Step 1

Given \(r=\text{No. of rows}=3\)

\(c=\text{No. of columns}=2\)

Step 2

\(\text{Degrees of freedom}=(r-1)\times(c-1)\)

\(dF=(3-1)\cdot(2-1)\)

\(d\cdot F=2\)

asked 2020-12-14

Find the expected count and the contribution to the chi-square statistic for the (Group 1, Yes) cell in the two-way table below.

\(\begin{array}{|c|c|c|}\hline&\text{Yes}&\text{No}&\text{Total}\\\hline\text{Group 1} &710 & 277 & 987\\ \hline\text{Group 2}& 1175 & 323&1498\\\hline \ \text{Total}&1885&600&2485 \\ \hline \end{array}\)

Round your answer for the excepted count to one decimal place, and your answer for the contribution to the chi-square statistic to three decimal places.

Expected count=?

contribution to the chi-square statistic=?

\(\begin{array}{|c|c|c|}\hline&\text{Yes}&\text{No}&\text{Total}\\\hline\text{Group 1} &710 & 277 & 987\\ \hline\text{Group 2}& 1175 & 323&1498\\\hline \ \text{Total}&1885&600&2485 \\ \hline \end{array}\)

Round your answer for the excepted count to one decimal place, and your answer for the contribution to the chi-square statistic to three decimal places.

Expected count=?

contribution to the chi-square statistic=?

asked 2021-06-13

1. Who seems to have more variability in their shoe sizes, men or women?

a) Men

b) Women

c) Neither group show variability

d) Flag this Question

2. In general, why use the estimate of \(n-1\) rather than n in the computation of the standard deviation and variance?

a) The estimate n-1 is better because it is used for calculating the population variance and standard deviation

b) The estimate n-1 is never used to calculate the sample variance and standard deviation

c) \(n-1\) provides an unbiased estimate of the population and allows more variability when using a sample and gives a better mathematical estimate of the population

d) The estimate n-1 is better because it is use for calculation of both the population and sample variance as well as standard deviation.

\(\begin{array}{|c|c|}\hline \text{Shoe Size (in cm)} & \text{Gender (M of F)} \\ \hline 25.7 & M \\ \hline 25.4 & F \\ \hline 23.8 & F \\ \hline 25.4 & F \\ \hline 26.7 & M \\ \hline 23.8 & F \\ \hline 25.4 & F \\ \hline 25.4 & F \\ \hline 25.7 & M \\ \hline 25.7 & F \\ \hline 23.5 & F \\ \hline 23.1 & F \\ \hline 26 & M \\ \hline 23.5 & F \\ \hline 26.7 & F \\ \hline 26 & M \\ \hline 23.1 & F \\ \hline 25.1 & F \\ \hline 27 & M \\ \hline 25.4 & F \\ \hline 23.5 & F \\ \hline 23.8 & F \\ \hline 27 & M \\ \hline 25.7 & F \\ \hline \end{array}\)

\(\begin{array}{|c|c|}\hline \text{Shoe Size (in cm)} & \text{Gender (M of F)} \\ \hline 27.6 & M \\ \hline 26.9 & F \\ \hline 26 & F \\ \hline 28.4 & M \\ \hline 23.5 & F \\ \hline 27 & F \\ \hline 25.1 & F \\ \hline 28.4 & M \\ \hline 23.1 & F \\ \hline 23.8 & F \\ \hline 26 & F \\ \hline 25.4 & M \\ \hline 23.8 & F \\ \hline 24.8 & M \\ \hline 25.1 & F \\ \hline 24.8 & F \\ \hline 26 & M \\ \hline 25.4 & F \\ \hline 26 & M \\ \hline 27 & M \\ \hline 25.7 & F \\ \hline 27 & M \\ \hline 23.5 & F \\ \hline 29 & F \\ \hline \end{array}\)

a) Men

b) Women

c) Neither group show variability

d) Flag this Question

2. In general, why use the estimate of \(n-1\) rather than n in the computation of the standard deviation and variance?

a) The estimate n-1 is better because it is used for calculating the population variance and standard deviation

b) The estimate n-1 is never used to calculate the sample variance and standard deviation

c) \(n-1\) provides an unbiased estimate of the population and allows more variability when using a sample and gives a better mathematical estimate of the population

d) The estimate n-1 is better because it is use for calculation of both the population and sample variance as well as standard deviation.

\(\begin{array}{|c|c|}\hline \text{Shoe Size (in cm)} & \text{Gender (M of F)} \\ \hline 25.7 & M \\ \hline 25.4 & F \\ \hline 23.8 & F \\ \hline 25.4 & F \\ \hline 26.7 & M \\ \hline 23.8 & F \\ \hline 25.4 & F \\ \hline 25.4 & F \\ \hline 25.7 & M \\ \hline 25.7 & F \\ \hline 23.5 & F \\ \hline 23.1 & F \\ \hline 26 & M \\ \hline 23.5 & F \\ \hline 26.7 & F \\ \hline 26 & M \\ \hline 23.1 & F \\ \hline 25.1 & F \\ \hline 27 & M \\ \hline 25.4 & F \\ \hline 23.5 & F \\ \hline 23.8 & F \\ \hline 27 & M \\ \hline 25.7 & F \\ \hline \end{array}\)

\(\begin{array}{|c|c|}\hline \text{Shoe Size (in cm)} & \text{Gender (M of F)} \\ \hline 27.6 & M \\ \hline 26.9 & F \\ \hline 26 & F \\ \hline 28.4 & M \\ \hline 23.5 & F \\ \hline 27 & F \\ \hline 25.1 & F \\ \hline 28.4 & M \\ \hline 23.1 & F \\ \hline 23.8 & F \\ \hline 26 & F \\ \hline 25.4 & M \\ \hline 23.8 & F \\ \hline 24.8 & M \\ \hline 25.1 & F \\ \hline 24.8 & F \\ \hline 26 & M \\ \hline 25.4 & F \\ \hline 26 & M \\ \hline 27 & M \\ \hline 25.7 & F \\ \hline 27 & M \\ \hline 23.5 & F \\ \hline 29 & F \\ \hline \end{array}\)

asked 2021-01-19

The following is a two-way table showing preferences for an award (A, B, C) by gender for the students sampled in survey. Test whether the data indicate there is some association between gender and preferred award.

\(\begin{array}{|c|c|c|}\hline &\text{A}&\text{B}&\text{C}&\text{Total}\\\hline \text{Female} &20&76&73&169\\ \hline \text{Male}&11&73&109&193 \\ \hline \text{Total}&31&149&182&360 \\ \hline \end{array}\\\)

Chi-square statistic=?

p-value=?

Conclusion: (reject or do not reject \(H_0\))

Does the test indicate an association between gender and preferred award? (yes/no)

\(\begin{array}{|c|c|c|}\hline &\text{A}&\text{B}&\text{C}&\text{Total}\\\hline \text{Female} &20&76&73&169\\ \hline \text{Male}&11&73&109&193 \\ \hline \text{Total}&31&149&182&360 \\ \hline \end{array}\\\)

Chi-square statistic=?

p-value=?

Conclusion: (reject or do not reject \(H_0\))

Does the test indicate an association between gender and preferred award? (yes/no)

asked 2021-06-05

Complete the two-way table.

\(\begin{array}{|c|cc|c|} \hline \text{ Gender } & \text { Response } & \text { } & \text {}\\ \hline & \text { Yes } & \text { No } & \text { Total } \\ \hline \text { Male } & & 52 & \\ \hline \text { Female } & 48 & & 110 \\ \hline \text { Total } & 65 & & \\ \hline \end{array}\)

asked 2021-05-09

Use the two-way table of data from another student survey to answer the following question.

Like Aerobic Exercise Like Weight Lifting Yes No Total Yes 7 14 21 No 12 7 19 Total 19 21 40

Find the conditional relative frequency that a student likes to lift weights, given that the student likes aerobics.

Like Aerobic Exercise Like Weight Lifting Yes No Total Yes 7 14 21 No 12 7 19 Total 19 21 40

Find the conditional relative frequency that a student likes to lift weights, given that the student likes aerobics.

asked 2020-11-26

A random sample of 2,500 people was selected, and the people were asked to give their favorite season. Their responses, along with their age group, are summarized in the two-way table below.

\(\begin{array}{c|cccc|c} & \text {Winter} &\text{Spring}& \text {Summer } & \text {Fall}& \text {Total}\\ \hline \text {Children} & 30 & 0 & 170&0&200 \\ \text{Teens} & 150 & 75 & 250&25&500 \\ \text {Adults } & 250 & 250 & 250&250&1000 \\ \text {Seniors} & 300 & 150 & 50&300&800 \\ \hline \text {Total} & 730 & 475 & 720 &575&2500 \end{array}\)

Among those whose favorite season is spring, what proportion are adults?

\(a) \frac{250}{1000}\)

\(b) \frac{250}{2500}\)

\(c) \frac{475}{2500}\)

\(d) \frac{250}{475}\)

\(e) \frac{225}{475}\)

\(\begin{array}{c|cccc|c} & \text {Winter} &\text{Spring}& \text {Summer } & \text {Fall}& \text {Total}\\ \hline \text {Children} & 30 & 0 & 170&0&200 \\ \text{Teens} & 150 & 75 & 250&25&500 \\ \text {Adults } & 250 & 250 & 250&250&1000 \\ \text {Seniors} & 300 & 150 & 50&300&800 \\ \hline \text {Total} & 730 & 475 & 720 &575&2500 \end{array}\)

Among those whose favorite season is spring, what proportion are adults?

\(a) \frac{250}{1000}\)

\(b) \frac{250}{2500}\)

\(c) \frac{475}{2500}\)

\(d) \frac{250}{475}\)

\(e) \frac{225}{475}\)

asked 2021-03-04

How are the smoking habits of students related to their parents' smoking? Here is a two-way table from a survey of student s in eight Arizona high schools:

\(\begin{array}{c|c}&\text{Student smokes}&\text{Student does not smoke}&\text{Total}\\\hline\text{Both parents smoke}&400&1380&400+1380=1780\\\hline\text{One parent smokes}&416&1823&416+1823=2239\\\hline\text{Neither parent smokes}&188&1168&188+1168=1356\\\hline\text{Total}&400+416+188=1004&1380+1823+1168=4371&1004+4371=5375\end{array}\)

(a) Write the null and alternative hypotheses for the question of interest.

(b) Find the expected cell counts. Write a sentence that explains in simple language what "expected counts" are.

(c) Find the chi-square statistic, its degrees of freedom, and the P-value.

(d) What is your conclusion about significance?

\(\begin{array}{c|c}&\text{Student smokes}&\text{Student does not smoke}&\text{Total}\\\hline\text{Both parents smoke}&400&1380&400+1380=1780\\\hline\text{One parent smokes}&416&1823&416+1823=2239\\\hline\text{Neither parent smokes}&188&1168&188+1168=1356\\\hline\text{Total}&400+416+188=1004&1380+1823+1168=4371&1004+4371=5375\end{array}\)

(a) Write the null and alternative hypotheses for the question of interest.

(b) Find the expected cell counts. Write a sentence that explains in simple language what "expected counts" are.

(c) Find the chi-square statistic, its degrees of freedom, and the P-value.

(d) What is your conclusion about significance?

asked 2021-05-14

Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.

\(\begin{array}{|c|c|}\hline 11.8 & 7.7 & 6.5 & 6 .8& 9.7 & 6.8 & 7.3 \\ \hline 7.9 & 9.7 & 8.7 & 8.1 & 8.5 & 6.3 & 7.0 \\ \hline 7.3 & 7.4 & 5.3 & 9.0 & 8.1 & 11.3 & 6.3 \\ \hline 7.2 & 7.7 & 7.8 & 11.6 & 10.7 & 7.0 \\ \hline \end{array}\)

a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. \([Hint.\ ?x_{j}=219.5.]\) (Round your answer to three decimal places.)

MPa

State which estimator you used.

\(x\)

\(p?\)

\(\frac{s}{x}\)

\(s\)

\(\tilde{\chi}\)

b) Calculate a point estimate of the strength value that separates the weakest \(50\%\) of all such beams from the strongest \(50\%\).

MPa

State which estimator you used.

\(s\)

\(x\)

\(p?\)

\(\tilde{\chi}\)

\(\frac{s}{x}\)

c) Calculate a point estimate of the population standard deviation ?. \([Hint:\ ?x_{i}2 = 1859.53.]\) (Round your answer to three decimal places.)

MPa

Interpret this point estimate.

This estimate describes the linearity of the data.

This estimate describes the bias of the data.

This estimate describes the spread of the data.

This estimate describes the center of the data.

Which estimator did you use?

\(\tilde{\chi}\)

\(x\)

\(s\)

\(\frac{s}{x}\)

\(p?\)

d) Calculate a point estimate of the proportion of all such beams whose flexural strength exceeds 10 MPa. [Hint: Think of an observation as a "success" if it exceeds 10.] (Round your answer to three decimal places.)

e) Calculate a point estimate of the population coefficient of variation \(\frac{?}{?}\). (Round your answer to four decimal places.)

State which estimator you used.

\(p?\)

\(\tilde{\chi}\)

\(s\)

\(\frac{s}{x}\)

\(x\)

\(\begin{array}{|c|c|}\hline 11.8 & 7.7 & 6.5 & 6 .8& 9.7 & 6.8 & 7.3 \\ \hline 7.9 & 9.7 & 8.7 & 8.1 & 8.5 & 6.3 & 7.0 \\ \hline 7.3 & 7.4 & 5.3 & 9.0 & 8.1 & 11.3 & 6.3 \\ \hline 7.2 & 7.7 & 7.8 & 11.6 & 10.7 & 7.0 \\ \hline \end{array}\)

a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. \([Hint.\ ?x_{j}=219.5.]\) (Round your answer to three decimal places.)

MPa

State which estimator you used.

\(x\)

\(p?\)

\(\frac{s}{x}\)

\(s\)

\(\tilde{\chi}\)

b) Calculate a point estimate of the strength value that separates the weakest \(50\%\) of all such beams from the strongest \(50\%\).

MPa

State which estimator you used.

\(s\)

\(x\)

\(p?\)

\(\tilde{\chi}\)

\(\frac{s}{x}\)

c) Calculate a point estimate of the population standard deviation ?. \([Hint:\ ?x_{i}2 = 1859.53.]\) (Round your answer to three decimal places.)

MPa

Interpret this point estimate.

This estimate describes the linearity of the data.

This estimate describes the bias of the data.

This estimate describes the spread of the data.

This estimate describes the center of the data.

Which estimator did you use?

\(\tilde{\chi}\)

\(x\)

\(s\)

\(\frac{s}{x}\)

\(p?\)

d) Calculate a point estimate of the proportion of all such beams whose flexural strength exceeds 10 MPa. [Hint: Think of an observation as a "success" if it exceeds 10.] (Round your answer to three decimal places.)

e) Calculate a point estimate of the population coefficient of variation \(\frac{?}{?}\). (Round your answer to four decimal places.)

State which estimator you used.

\(p?\)

\(\tilde{\chi}\)

\(s\)

\(\frac{s}{x}\)

\(x\)

asked 2020-10-26

In this exercise , a two-way table is shown for two groups , 1 and 2 , and two possible outcomes , A nad B
\(\begin{array}{|c|c|c|}\hline &\text{Outcome A}&\text{Outcome B}&\text{Total}\\\hline \text{Group 1} &30&20&50\\ \hline \text{Group 2}&40&110&150\\ \hline \text{Total}&70&130&200\\ \hline \end{array}\\\)

a) What proportion of all cases had Outcome A?

b) What proportion of all cases are in Group 1?

c) What proportion of cases in group 1 had Outcome B?

d) What proportion of cases who had Outcome A were in group 2?

a) What proportion of all cases had Outcome A?

b) What proportion of all cases are in Group 1?

c) What proportion of cases in group 1 had Outcome B?

d) What proportion of cases who had Outcome A were in group 2?

asked 2021-05-23

The two-way table shows the eye color of 200 cats participating in a cat show.

\( \begin{array}{|l|c|c|c|c|} \hline & \text { Green } & \text { Blue } & \text { Yellow } & \text { Total } \\ \hline \text { Male } & 40 & 24 & 16 & 80 \\ \hline \text { Female } & 30 & 60 & 30 & 120 \\ \hline \text { Total } & 70 & 84 & 46 & 200 \\ \hline \end{array}\)

Make a two-way relative frequency table to show the distribution of the data with respect to gender. Round to the nearest tenth of a percent, as needed.