Understanding Basic Statistics
Understanding Basic Statistics
7th Edition
ISBN: 9781305254060
Author: Charles Henry Brase, Corrinne Pellillo Brase
Publisher: Cengage Learning
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Chapter 11.4, Problem 7P

(a)

To determine

To test: The verification of x=439,y=280,x2=32.393,y2=13.142,

xy=20.599,r0.784.

(a)

Expert Solution
Check Mark

Answer to Problem 7P

Solution: It is verified that, x=439,y=280,x2=32.393,y2=13.142,

xy=20.599,r0.784.

Explanation of Solution

Calculation: Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season.

The following table shows the x,y,x2,y2,xy:

x y x2 y2 xy
67 44 4489 1936 2948
65 42 4225 1764 2730
75 48 5625 2304 3600
86 51 7396 2601 4386
73 44 5329 1936 3212
73 51 5329 2601 3723
439 280 32393 13142 20599

In above table, the last column shows the total of corresponding column.

So, x=439,y=280,x2=32,393,y2=13,142, xy=20,599.

The correlation coefficient, r is calculated as follows:

r=n(xy)(x)(y)[nx2(x)2][ny2(y)2]=6(20599)(439)(280)[6(32393)(439)2][6(13142)(280)2]=674860.18840.784

Conclusion: Hence, it is verified that,

x=439,y=280,x2=32.393,y2=13.142, xy=20.599,r0.784.

(b)

To determine

To test: The claim that ρ>0 at 0.05 level of significance.

(b)

Expert Solution
Check Mark

Answer to Problem 7P

Solution: We have sufficient evidence to conclude that the population correlation coefficient between x and y is positive at 5% level of significance.

Explanation of Solution

Calculation: Using the level of significance, α=0.05.

The null hypothesis for testing is defined as,

H0:ρ=0

The alternative hypothesis is defined as,

H1:ρ>0

The sample test statistic is,

t=rn21r2=0.784621(0.784)22.526

The degrees of freedom are d.f.=n2=62=4

The abovetest is right tailed test, so we can use the one-tail area in the student’s distributiontable (Table 4 of the Appendix). From table, the range of p-value for the sample test statistic t=2.526 is 0.025<P-value<0.05. Since the interval containing the P-value is less than 0.05, hencewe have to reject the null hypothesis at α=0.05. Therefore, we can conclude that the data is statistically significant at 0.05 level of significance.

Conclusion: We have sufficient evidence to conclude that the population correlation coefficient between x and y is positive at 5% level of significance.

(c)

To determine

To test: The verification of Se2.6964,a16.542,b0.4117 and x¯=73.167

(c)

Expert Solution
Check Mark

Answer to Problem 7P

Solution: It is verified that, Se2.6964,a16.542,b0.4117 and x¯=73.167.

Explanation of Solution

Calculation: The results obtained in part (a) are,

n=6,x=439,y=280,x2=32,393,y2=13,142, xy=20,599.

Now, a,b,Se are calculated as follows:

b=n(xy)(x)(y)nx2(x)2=6(20599)(439)(280)6(32393)(439)2=6741637=0.411730.4117

x¯=xn=439673.167

y¯=yn=280646.667

a=y¯bx¯=46.6670.4117(73.167)16.54

Se=y2aybxyn2=1314216.54(280)0.4117(20599)62=0.269592.696

Conclusion: Hence, it is verified that, Se2.6964,a16.542,b0.4117 and x¯=73.167

(d)

To determine

To find: The predicted percentage y^ of successful field goals for a player with x=70% successful free throws.

(d)

Expert Solution
Check Mark

Answer to Problem 7P

Solution: The predicted percentage y^ of successful field goals for a player with x=70% successful free throws is 45.36%.

Explanation of Solution

Calculation: The results obtained in above part are a16.54,b0.4117

The regression line equation is y^=a+bx,

y^=16.54+0.4117x

Now to find the predicted y^ when x=70%

y^=16.54+0.4117(70)45.36

Interpretation: The predicted percentage y^ of successful field goals for a player with x=70% successful free throws is 45.36%.

(e)

To determine

To find: The 90% confidence interval for y when x=70.

(e)

Expert Solution
Check Mark

Answer to Problem 7P

Solution: The 90% confidence interval for y when x=70 is (39.06,51.67).

Explanation of Solution

Calculation: The find 90% confidence interval for y when x=70 by using MINITAB software is as:

Step 1: Go to Stat >Regression>Regression > Predict.

Step 2: Select ‘y’ in Response and write 70 in ‘x’ box.

Step 3: Click on Options write 90 in ‘Confidence level’ and select ‘Two-sided’ in Type of interval. Then click on OK.

The 90% confidence interval is obtained as: (39.06,51.67).

Interpretation: The 90% confidence interval for y when x=70 is (39.06,51.67).

(f)

To determine

To test: The claim that β>0 at 0.05 level of significance.

(f)

Expert Solution
Check Mark

Answer to Problem 7P

Solution: We have sufficient evidence to conclude that the slopeis positive at 5% level of significance.

Explanation of Solution

Calculation: Using the level of significance, α=0.05.

The null hypothesis for testing is defined as,

H0:β=0

The alternative hypothesis is defined as,

H1:β>0

The find t statistic and P-value using MINITAB software is as:

Step 1: Enter x and y in Minitab worksheet.

Step 2: Go to Stat > Regression > Regression >Fit Regression Model.

Step 2: Select ‘y’ in Response and ‘x’ in ‘Continuous predictors’ box. Then click on OK.

The sample test statistic is t=2.52 and P-value is 0.065.

The software gives the P-value for two-tailed test, for finding the p-value for one tailed testwe can divide the obtained P-value by 2.

Pvalue for one tailed test=0.0652=0.0325.

Since P-value is less than 0.05, hence we can reject the null hypothesis at α=0.05. Therefore, we can conclude that the data is statistically significant at 0.05 level of significance.

Conclusion: We have sufficient evidence to conclude that the slopeis positive at 5% level of significance.

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Chapter 11 Solutions

Understanding Basic Statistics

Ch. 11.1 - For Problems 9-19, please provide the following...Ch. 11.1 - For Problems 9-19. please provide the following...Ch. 11.1 - For Problems 9-19. please provide the following...Ch. 11.1 - For Problems 9-19. please provide the following...Ch. 11.1 - For Problems 9-19. please provide the following...Ch. 11.1 - For Problems 9-19. please provide the following...Ch. 11.1 - Prob. 17PCh. 11.1 - Prob. 18PCh. 11.1 - Prob. 19PCh. 11.2 - Statistical Literacy For a chi-square...Ch. 11.2 - Statistical Literacy How are expected frequencies...Ch. 11.2 - Statistical Literacy Explain why goodness-of-fit...Ch. 11.2 - Critical Thinking When the sample evidence is...Ch. 11.2 - For Problems 5-14, please provide the following...Ch. 11.2 - For Problems 5-14, please provide the following...Ch. 11.2 - For Problems 5-14, please provide the following...Ch. 11.2 - For Problems 5-14, please provide the following...Ch. 11.2 - For Problems 5-14, please provide the following...Ch. 11.2 - Prob. 10PCh. 11.2 - Prob. 11PCh. 11.2 - For Problems 5-14, please provide the following...Ch. 11.2 - Prob. 13PCh. 11.2 - Prob. 14PCh. 11.3 - Statistical Literacy Docs the x distribution need...Ch. 11.3 - Prob. 2PCh. 11.3 - Prob. 3PCh. 11.3 - For Problems 3-11, please provide the following...Ch. 11.3 - For Problems 3-11. please provide the following...Ch. 11.3 - For Problems 3-11. please provide the following...Ch. 11.3 - Prob. 7PCh. 11.3 - For Problems 3-11, please provide the following...Ch. 11.3 - For Problems 3-11. please provide the following...Ch. 11.3 - Prob. 10PCh. 11.3 - Prob. 11PCh. 11.4 - Prob. 1PCh. 11.4 - Statistical Literacy What is the symbol used for...Ch. 11.4 - Prob. 3PCh. 11.4 - Statistical Literacy How does the t value for the...Ch. 11.4 - Prob. 5PCh. 11.4 - Using Computer Printouts Problems 5 and 6 use the...Ch. 11.4 - Prob. 7PCh. 11.4 - In Problems 7-12, parts (a) and (b) relate to...Ch. 11.4 - In Problems 7-12, parts (a) and (b) relate to...Ch. 11.4 - In Problems 7-12, parts (a) and (b) relate to...Ch. 11.4 - Prob. 11PCh. 11.4 - Prob. 12PCh. 11.4 - Prob. 13PCh. 11.4 - Prob. 14PCh. 11.4 - Prob. 15PCh. 11.4 - Prob. 16PCh. 11.4 - Prob. 17PCh. 11.4 - Prob. 18PCh. 11.4 - Prob. 19PCh. 11 - Statistical Literacy of the following random...Ch. 11 - Prob. 2CRCh. 11 - Prob. 3CRCh. 11 - Before you solve Problems 6-10, first classify the...Ch. 11 - Prob. 5CRCh. 11 - Before you solve Problems 6-10, first classify the...Ch. 11 - Before you solve Problems 6-10, first classify the...Ch. 11 - Prob. 8CRCh. 11 - Prob. 9CRCh. 11 - Prob. 10CRCh. 11 - Prob. 11CRCh. 11 - The Statistical Abstract of the United States...Ch. 11 - Prob. 1LCWPCh. 11 - Prob. 2LCWPCh. 11 - Prob. 3LCWPCh. 11 - Prob. 4LCWPCh. 11 - Prob. 1CRPCh. 11 - Prob. 2CRPCh. 11 - Prob. 3CRPCh. 11 - Prob. 4CRPCh. 11 - Prob. 5CRPCh. 11 - Prob. 6CRPCh. 11 - Prob. 7CRP
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