MATH 122 Exam 4

Here is a bivariate data set in which you believe y to be the response variable. Make a scatter plot of this data. Which point appears to be an outlier?

(-55.6,-1.1)

A random sample of 22 pre-school children was taken. The child was asked to draw a nickel. The diameter of that nickel was recorded. Their parent's incomes (in thousands of $) and the diameter of the nickel they drew are given below. (table displayed here) Test the claim that there is significant correlation at the 0.05 significance level. Retain at least 3 decimals on all values. a) Identify the correct alternative hypothesis. H1:r≠0 H1:pL≠pH H1:μ≠0 H1:ρ≠0 H1:ρ=0 b) The r test statistic value is: c) The critical value is: d) Based on this, we Reject H0 Fail to reject H0 e) Which means There is not sufficient evidence to warrant rejection of the claim There is sufficient evidence to warrant rejection of the claim There is not sufficient evidence to support the claim The sample data supports the claim f) The regression equation (in terms of income x) is:ˆy= g) To predict what diameter a child would draw a nickel given family income, it would be most appropriate to: Use the regression equation Use the mean coin size Use the P-Value Use the residual

a. H1:ρ≠0 b. -0.40177668462731 c. 0.423 or -0.423 d. Fail to reject H0 e. There is not sufficient evidence to support the claim f. −0.071376035304276⋅x+26.20252281376 g. Use the mean coin size

Suppose you were to collect data for the following pair of variables, people: age, grip strength. You want to make a scatterplot. Which variable would you use as the explanatory variable? age grip strength Which variable would you use as the response variable? age grip strength Would you expect to see a positive or negative association? positive negative neither

age grip strength neither

Match each scatterplot shown below with one of the four specified correlations. a. -0.05 b. -0.99 c. -0.22 d. 0.99

d c a b

If your null and alternative hypothesis are: H0:ρ=0 H1:ρ<0 Then the test is: If we reject the null hypothesis, that would suggest the data has a significant:

left tailed decreasing trend

An institute conducted a clinical trial of its methods for gender selection. The results showed that 345 of 601 babies born to parents using a specific​ gender-selection method were boys. Use the sign test and a 0.1 significance level to test the claim that the method increased the likelihood of having a boy. Find the null and alternative hypothesis. H0: p>0.5 p=0.5 p<0.5 p≠0.5 H1: p=0.5 p≠0.5 p>0.5 p<0.5 If we consider + to represent a boy, then how many of each sign is there? Positive Signs: Negative signs: Total Signs: What is the p-value? What is the conclusion about the null? What is the conclusion about the claim?

p=0.5 p>0.5 345 256 601 0 Reject the null hypothesis Support the claim that the method increased the likelihood of having a boy

Adults randomly selected for a poll were asked if they​ "favor or oppose using federal tax dollars to fund medical research using stem cells obtained from human​ embryos." Of the subjects​ surveyed, 255 were in​ favor, 280 were​ opposed, and 91 were unsure. A politician claims that people​ don't really understand the stem cell issue and their responses to such questions are random responses equivalent to a coin flip. Use a 0.05 significance level to test the claim that the proportion of subjects who respond in favor is equal to 0.5. Find the null and alternative hypothesis. H0: p<0.5 p≠0.5 p>0.5 p=0.5 H1: p>0.5 p<0.5 p≠0.5 p=0.5 If we consider + to represent those in favor, then how many of each sign is there? Positive Signs: Negative Signs: Total Signs: What is the p-value? (make sure to times by 2) What is the conclusion about the null? What is the conclusion about the claim?

p=0.5 p≠0.5 255 280 535 .299 Fail to reject the null hypothesis Fail to reject the claim that the proportion of subjects who respond in favor is equal to 0.5

Here is a bivariate data set. Find the correlation coefficient and report it accurate to three decimal places. r = What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place. r² = _____%

r= -0.627 r² = 39.3%

You wish to determine if there is a linear correlation between the two variables at a significance level of α=0.05α. You have the following bivariate data set. xy table displayed here What is the critival value for this hypothesis test? rc.v. = What is the correlation coefficient for this data set? r = Your final conclusion is that... There is insufficient sample evidence to support the claim the there is a correlation between the two variables. There is sufficient sample evidence to support the claim that there is a statistically significant correlation between the two variables.

rc.v. = 0.482 r = -0.976 There is sufficient sample evidence to support the claim that there is a statistically significant correlation between the two variables.

You are conducting a multinomial Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies: Ho : pA=0.3; pB=0.4; pC=0.15; pD=0.15 Complete the table. Report all answers accurate to three decimal places (table displayed below) What is the chi-square test-statistic for this data? χ2= What is the P-Value? P-Value = For significance level alpha 0.005, what would be the conclusion of this hypothesis test? Fail to reject the Null Hypothesis Reject the Null Hypothesis

x2 = 40.618 p-value = 0

You are conducting a multinomial Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies: Ho: pA=0.1; pB=0.4; pC=0.3; pD=0.2 table displayed here Complete the table. Report all answers accurate to three decimal places. What is the chi-square test-statistic for this data? χ2= What is the P-Value? P-Value = For significance level alpha 0.1, what would be the conclusion of this hypothesis test? Reject the Null Hypothesis Fail to reject the Null Hypothesis

x2 = 56.893 p-value = 0 Reject the Null Hypothesis

An experiment is run. The mass of an object is recorded over time. (table displayed) Using your calculator, run a linear regression to determine the equation of the line of best fit. Regression Equation: Enter the equation in slope-intercept form (y=mx+b) with parameters accurate to three decimal places.

y= −0.671x + 59.56

Based on the data shown below, calculate the regression line. Regression Equation: _______ Enter the equation in slope-intercept form (y=mx+b)(y=mx+b) with parameters accurate to three decimal places. (x/y table displayed here)

y=4x+9

Based on the data shown below, calculate the regression line. Regression Equation: Enter the equation in slope-intercept form (y=mx+b) with parameters accurate to three decimal places. x/y table displayed here

y=8x+12

Based on the data shown below, calculate the regression line. Regression Equation: Enter the equation in slope-intercept form (y=mx+b)(y=mx+b) with parameters accurate to three decimal places. xy table displayed here

y=9x+4

You conduct a one-factor ANOVA with 8 groups and 10 subjects in each group (a balanced design) and obtain F=2.16. Find the requested values. dfbetween= dfwithin=

7 72

The following is data for the first and second Quiz scores for 8 students in a class. Table displayed here plot the points on the grid Predict the value of the second quiz score (at the 0.05 significance level) if a student had a score of 12 on the first test.

9.6557332974862

You wish to determine if there is a linear correlation between the two variables at a significance level of α=0.02α=0.02. You have the following bivariate data set. (table displayed here) What is the correlation coefficient for this data set? r = What is the p-value for this correlation coefficient? p-value = Your final conclusion is that... There is sufficient sample evidence to support the claim that there is a statistically significant correlation between the two variables. There is insufficient sample evidence to support the claim the there is a correlation between the two variables.

-0.992 0 There is sufficient sample evidence to support the claim that there is a statistically significant correlation between the two variables.

Here is a bivariate data set. Find the correlation coefficient and report it accurate to three decimal places. r=

-0.302

The following data includes the year, make, model, mileage (in thousands of miles) and asking price (in US dollars) for each of 13 used Honda Odyssey minivans. The data was collected from the Web site of the Seattle P-I on April 25, 2005. Compute the correlation between mileage and price for these minivans. (Assume the correlation conditions have been satisfied and round your answer to three decimal places.) r=

-0.873

Here is a bivariate data set. xy table displayed here Find the correlation coefficient and report it accurate to three decimal places. r=

-0.952

The following is data for the first and second Quiz scores for 8 students in a class. (table displayed here) Predict the value of the second quiz score (at the 0.05 significance level) if a student had a score of 3838 on the first test.

35.23423255814

You run a regression analysis on a bivariate set of data (n=81). You obtain the regression equation y=−3.382x+26.212 with a correlation coefficient of r=−0.908 (which is significant at α=0.01). You want to predict what value (on average) for the explanatory variable will give you a value of 30 on the response variable. What is the predicted explanatory value?

-1.1

You run a regression analysis on a bivariate set of data (n=85). You obtain the regression equation y=−2.608x+−40.677 with a correlation coefficient of r=−0.897 (which is significant at α=0.01). You want to predict what value (on average) for the explanatory variable will give you a value of 30 on the response variable. What is the predicted explanatory value? x =

-27.1

You wish to conduct a hypothesis test to determine if a bivariate data set has a significant correlation among the two variables. That is, you wish to test the claim that there is a correlation (Ha:ρ≠0). You have a data set with 16 subjects, in which two variables were collected for each subject. You will conduct the test at a significance level of α=0.01α=0.01.Find the critical value for this test. rc.v. = ±

.623 link to critical r values https://researchbasics.education.uconn.edu/r_critical_value_table/

You wish to conduct a hypothesis test to determine if a bivariate data set has a significant correlation among the two variables. That is, you wish to test the claim that there is a correlation (Ha:ρ≠0). You have a data set with 6 subjects, in which two variables were collected for each subject. You will conduct the test at a significance level of α=0.05. Find the critical value for this test. rc.v. = ±

.811

You wish to determine if there is a linear correlation between the two variables at a significance level of α=0.005. You have the following bivariate data set. x/y table displayed here What is the correlation coefficient for this data set? r = What is the p-value for this correlation coefficient? p-value = Your final conclusion is that... There is sufficient sample evidence to support the claim that there is a statistically significant correlation between the two variables. There is insufficient sample evidence to support the claim the there is a correlation between the two variables.

0.028 0.924 There is insufficient sample evidence to support the claim the there is a correlation between the two variables.

On December 17, 2007 baseball writer John Hickey wrote an article for the Seattle P-I about increases to ticket prices for Seattle Mariners games during the 2008 season. The article included a data set that listed the average ticket price for each MLB team, the league in which the team plays (AL or NL), the number of wins during the 2007 season and the cost per win (in dollars). The data for the 16 National League teams are shown below. (table on other side) r=

0.101

You wish to conduct a hypothesis test to determine if a bivariate data set has a significant correlation among the two variables. That is, you wish to test the claim that there is a correlation (Ha:ρ≠0). You have a data set with 52 subjects, in which two variables were collected for each subject. You will conduct the test at a significance level of α=0.01 rc.v. = ±_____________________

0.354

At a .01 significance level with a sample size of 37, find the critical value for the correlation coefficient

0.418

At a .01 significance level with a sample size of 22, find the critical value for the correlation coefficient

0.537

You wish to determine if there is a linear correlation between the two variables at a significance level of α=0.01α=0.01. You have the following bivariate data set. (table displayed) What is the critical value for this hypothesis test? rc.v. = What is the correlation coefficient for this data set? r = Your final conclusion is that... There is sufficient sample evidence to support the claim that there is a statistically significant correlation between the two variables. There is insufficient sample evidence to support the claim the there is a correlation between the two variables.

0.623 -0.103 There is insufficient sample evidence to support the claim the there is a correlation between the two variables.

Based on the data shown below, calculate the correlation coefficient (to three decimal places) x/y table displayed here r=

0.98765966635685

You intend to conduct an ANOVA with 6 groups in which each group will have the same number of subjects: n=12. (This is referred to as a "balanced" single-factor ANOVA.) What are the degrees of freedom for the numerator? d.f.(treatment) = What are the degrees of freedom for the denominator? d.f.(error) =

5 66

You intend to conduct a goodness-of-fit test for a multinomial distribution with 8 categories. You collect data from 81 subjects. What are the degrees of freedom for the χ2 distribution for this test? d.f. =

7

A researcher uses an ANOVA to compare eight treatment conditions with a sample size of n = 14 in each treatment. For this analysis find the degrees of freedom. What is df(treatment)? This is sometimes referred to as the "numerator degrees of freedom." What is df(error)? This is sometimes referred to as the "denominator degrees of freedom." If the scenario was changed so that there were still eight treatments, but there were different sample sizes for each treatment (a.k.a. an unbalanaced design), which of the following degrees of freedom would NOT change? df(treatment) df(error) both change neither change

7 104 df(treatment)

You intend to conduct a goodness-of-fit test for a multinomial distribution with 3 categories. You collect data from 77 subjects. What are the degrees of freedom for the χ2 distribution for this test? d.f. =

2

You intend to conduct an ANOVA with 3 groups in which each group will have the same number of subjects: n=17. (This is referred to as a "balanced" single-factor ANOVA.) What are the degrees of freedom for the numerator? d.f.(treatment) = What are the degrees of freedom for the denominator? d.f.(error) =

2 48

Run a regression analysis on the following bivariate set of data with y as the response variable. (table displayed here) Predict what value (on average) for the response variable will be obtained from a value of 75.1 as the explanatory variable. Use a significance level of α=0.05 to assess the strength of the linear correlation. What is the predicted response value? y =

20.3

A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y). The results of the regression were: y=ax+b a=-0.988 b=27.409 r2=0.904401 r=-0.951 n=21 Use this to predict the number of situps a person who watches 0.5 hours of TV can do (to one decimal place)

26.915

You intend to conduct a test of independence for a contingency table with 4 categories in the column variable and 2 categories in the row variable. You collect data from 130 subjects. What are the degrees of freedom for the χ2 distribution for this test? d.f. =

3

Google Sheets can be used to find the critical value for an F distribution for a given significance level. For example, to find the critical value (the value above which you would reject the null hypothesis) for α=0.05 with dfbetween=6 and dfwithin=84, enter =FINV(0.05,6,84) Enter this into Google Sheets to confirm you obtain the value 2.209. You conduct a one-factor ANOVA with 4 groups and 8 subjects in each group (a balanced design). Use Google Sheets to find the critical values for α=0.05 and α=0.02 (report accurate to 3 decimal places). F0.05= F0.02=

F0.05 = 2.9466853008236 F0.02 = 3.850971753694

You are given a contingency table laying out the success and failure amounts of various treatments for a disease. You wish to test the following claim that success of the treatment is independent of the type of treatment. Which of the following would be your hypotheses? H0: Success and treatment are dependent. H1: Success is independent of treatment.< H0: Success is independent of treatment. H1: Success and treatment are dependent. H0: The proportion of success is the same in each treatment. H1: The proportion of success is NOT the same in each treatment. H0: The proportion of success is NOT the same in each treatment. H1: The proportion of success is the same in each treatment.

H0: Success is independent of treatment. H1: Success and treatment are dependent.

A national consumer magazine reported the following correlations. The correlation between car weight and car reliability is -0.5. The correlation between car weight and annual maintenance cost is 0.2. According to this information, which of the following statements are true? I. Heavier cars tend to be less reliable. II. Heavier cars tend to cost more to maintain. III. Car weight is related more strongly to reliability than to maintenance cost. I only II only III only I and II I, II, and III

I, II, and III

The table below contains the data for the amounts (in oz) in cans of a certain soda. The cans are labeled to indicate that the contents are 12 oz of soda. Use the sign test and a 0.1 significance level to test the claim that cans of this soda are NOT filled so that the median amount is 12 oz. Find the null and alternative hypothesis. H0: Median volume≠12 Median volume<12 Median volume>12 Median volume=12 H1: Median volume=12 Median volume>12 Median volume≠12 Median volume<12 If we consider + to represent a can having more than 12 oz. of soda, then how many of each sign is there? Positive Signs: Negative signs: Total Signs: What is the p value? What is the conclusion about the null? What is the conclusion about the claim?

Median volume=12 Median volume≠12 14 26 40 .081 Reject the null hypothesis... since .081 < 0.1 Support the claim that cans of this soda are NOT filled so that the median amount is 12 oz. NOTE: Do not include 12, as it is the median, and should not be considered in the sign value or total signs.

In testing a new drug, we obtained the following results: table displayed here Run the ANOVA and fill in the summary table with the results obtained: (Report P-value & F-ratio accurate to 3 decimal places and all other values accurate to 2 decimal places.) What conclusion can be drawn at the 0.1 significance level? The various drugs have results that are statistically different. The various drugs do not have results that are statistically different.

The various drugs have results that are statistically different.

In testing a new drug, we obtained the following results: table displayed here Run the ANOVA and fill in the summary table with the results obtained: What conclusion can be drawn at the 0.01 significance level? The various drugs do not have results that are statistically different. The various drugs have results that are statistically different.

The various drugs have results that are statistically different.

You are conducting a test of the claim that the row variable and the column variable are dependent in the following contingency table. The chi-square test-statistic for this data is 1.867. The critical value for this test of independence when using a significance level of αα = 0.05 is χ2= 5.991. What is the correct conclusion of this hypothesis test at the 0.05 significance level? There is sufficient evidence to support the claim that the row and column variables are dependent. There is sufficient evidence to warrant rejection of the claim that the row and column variables are dependent. There is not sufficient evidence to support the claim that the row and column variables are dependent. There is not sufficient evidence to warrant rejection of the claim that the row and column variables are dependent.

There is not sufficient evidence to support the claim that the row and column variables are dependent.

You are conducting a test of the claim that the row variable and the column variable are dependent in the following contingency table. The chi-square test-statistic for this data is 22.602. The critical value for this test of independence when using a significance level of αα = 0.005 is χ2= 10.597. What is the correct conclusion of this hypothesis test at the 0.005 significance level? There is sufficient evidence to support the claim that the row and column variables are dependent. There is not sufficient evidence to support the claim that the row and column variables are dependent. There is sufficient evidence to warrant rejection of the claim that the row and column variables are dependent. There is not sufficient evidence to warrant rejection of the claim that the row and column variables are dependent.

There is sufficient evidence to support the claim that the row and column variables are dependent.

Suppose you were to collect data for the following pair of variables, skin diving: depth, visibility. You want to make a scatterplot. Which variable would you use as the explanatory variable? depth visibility Which variable would you use as the response variable? depth visibility Would you expect to see a positive or negative association? positive negative neither

depth visibility negative

Place the steps of conducting a correlation hypothesis test in order. Match each step on the left with the procedure at that step on the right. Step 1. ----- 2. ----- 3. ----- 4. ----- 5. ----- 6. ----- 7. ----- a. compare the absolute value of the test statistic to the critical value b. find the critical value from the table c. reject or fail to reject the null hypothesis d. find the value of r (correlation coefficient) from your calculator e. write null and alternative hypotheses f. conclude there is a linear correlation or not sufficient evidence to conclude there is a linear correlation g. select a significance level alpha

e g d b a c f

The following data represent the results from an independent-measures experiment comparing three treatment conditions with n=4 in each sample. Conduct an analysis of variance with α=0.05 to determine whether these data are sufficient to conclude that there are significant differences between the treatments. 3 column table displayed here f-ratio= p-value= Conclusion: These data do not provide evidence of a difference between the treatments There is a significant difference between treatments n2 = To calculate η2η2 you can find the directions in the Learning Activities for Module 16. The directions are within the paragraph that starts with "Another value that sometimes gets calculated..." The results above were obtained because the sample means are close together. To construct the data set below, the same scores from above were used, then the size of the mean differences were increased. In particular, the first treatment scores were lowered by 2 points, and the third treatment scores were raised by 2 points. As a result, the three sample means are now much more spread out. Before you begin the calculation, predict how the changes in the data should influence the outcome of the analysis. That is, how will the F-ratio for these data compare with the F-ratio from above? 3 column table displayed here f-ratio= p-value= Conclusion: These data do not provide evidence of a difference between the treatments There is a significant difference between treatments n2 =

f-ratio = 0.85714285714286 p-value = 0.45631 These data do not provide evidence of a difference between the treatments n2 = 0.16 ----------------- f-ratio = 7.7142857142857 p-value = 0.01118 There is a significant difference between treatments n2 = 0.63157894736842

You are conducting a multinomial hypothesis test (α = 0.05) for the claim that all 5 categories are equally likely to be selected. The p-value for this sample is 0.1226 This test statistic leads to a decision to... reject the null accept the null fail to reject the null accept the alternative

fail to reject the null There is not sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected. If the p-value is greater than alpha, you accept the null hypothesis. If it is less than alpha, you reject the null hypothesis.

ANOVA is a statistical procedure that compares two or more treatment conditions for differences in variance. True False

false

You are conducting a multinomial hypothesis test (α = 0.05) for the claim that all 5 categories are equally likely to be selected. The p-value for this sample is 0.0347 This test statistic leads to a decision to... reject the null accept the null fail to reject the null accept the alternative As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected. There is not sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected. The sample data support the claim that all 5 categories are equally likely to be selected. There is not sufficient sample evidence to support the claim that all 5 categories are equally likely to be selected.

reject the null There is sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected.

You are conducting a multinomial hypothesis test (α = 0.05) for the claim that all 5 categories are equally likely to be selected. The p-value for this sample is 0.0008 This test statistic leads to a decision to... reject the null accept the null fail to reject the null accept the alternative As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected. There is not sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected. The sample data support the claim that all 5 categories are equally likely to be selected. There is not sufficient sample evidence to support the claim that all 5 categories are equally likely to be selected.

reject the null There is sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected.

Note that a significantly large F-ratio is evidence against equal population means. Thus, ANOVA hypothesis tests are always ____-tailed. left right one two

right

If your null and alternative hypothesis are: H0:ρ=0 H1:ρ>0 Then the test is: left tailed right tailed If we reject the null hypothesis, that would suggest the data has a significant: Increasing trend Decreasing trend

right tailed increasing trend

You are conducting a test of the claim that the row variable and the column variable are dependent in the following contingency table. x,y,z table displayed here Give all answers rounded to 3 places after the decimal point, if necessary. (a) Enter the expected frequencies below: Fill in table To find the expected frequencies: 1. Enter the observed matrix into the calculator, per the Technology Corner. 2. Perform the test, per the Technology Corner. 3. Return to the matrix menu and view the B matrix. This will be the expected frequencies. (b) What is the chi-square test-statistic for this data?Test Statistic: χ2= (c) What is the critical value for this test of independence when using a significance level of α = 0.10? Critical Value: χ2= (Enter 4.605 as the answer to this question.) (d) What is the correct conclusion of this hypothesis test at the 0.10 significance level? There is sufficient evidence to warrant rejection of the claim that the row and column variables are dependent. There is not sufficient evidence to warrant rejection of the claim that the row and column variables are dependent. There is not sufficient evidence to support the claim that the row and column variables are dependent. There is sufficient evidence to support the claim that the row and column variables are dependent.

test- stat χ2≈16.927 critical value χ2=4.605 Conclusion: There is sufficient evidence to support the claim that the row and column variables are dependent.