Question

In: Statistics and Probability

The number of hours 10 students spent studying for a test and their scores on that...

The number of hours 10 students spent studying for a test and their scores on that test are shown in the table. Is there enough evidence to conclude that there is a significant linear correlation between the data? Use alphaequals0.05.

Hours, x= 0 1 2 4 4 5 5 6 7 8 Test score, y= 41 40 51 56 65 70 76 70 84 97

1. Setup the hypothesis for the test.

2. Identify the critical value(s). Select the correct choice below and fill in any answer boxes within your choice The critical value is ____ Or The critical values are -t0=____ &t0=____

3. Calculate the test statistic. T=_____(Round to three decimal places as needed)

4. What is your conclusion? There ____(is or is not) enough evidence at the 5% level of significance to conclude that there____ (is is not) a significant linear correlation between vehicle weight and variability in braking distance on a dry surface.

Solutions

Expert Solution

X Y XY
0 41 0 0 1681
1 40 40 1 1600
2 51 102 4 2601
4 56 224 16 3136
4 65 260 16 4225
5 70 350 25 4900
5 76 380 25 5776
6 70 420 36 4900
7 84 588 49 7056
8 97 776 64 9409
Ʃx = 42
Ʃy = 650
Ʃxy = 3140
Ʃx² = 236
Ʃy² = 45284
Sample size, n = 10
x̅ = Ʃx/n = 42/10 = 4.2
y̅ = Ʃy/n = 650/10 = 65
SSxx = Ʃx² - (Ʃx)²/n = 236 - (42)²/10 = 59.6
SSyy = Ʃy² - (Ʃy)²/n = 45284 - (650)²/10 = 3034
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 3140 - (42)(650)/10 = 410

Slope, b = SSxy/SSxx = 410/59.6 = 6.8791946

y-intercept, a = y̅ -b* x̅ = 65 - (6.87919)*4.2 = 36.107383

Regression equation :

ŷ = 36.1074 + (6.8792) x

Sum of Square error, SSE = SSyy -SSxy²/SSxx = 3034 - (410)²/59.6 = 213.5302013

Standard error, se = √(SSE/(n-2)) = √(213.5302/(10-2)) = 5.16636

--

1.

Null and alternative hypothesis:

Ho: β₁ = 0

Ha: β₁ ≠ 0

2.

df = n-2 = 8

Critical value, t_c = T.INV.2T(0.05, 8) = 2.306

The critical values are -t0 = -2.306 & t0 = 2.306

3.

Test statistic:

t = b/(se/√SSxx) = 10.280

4.

Conclusion:

There is enough evidence at the 5% level of significance to conclude that there is a significant linear correlation between vehicle weight and variability in braking distance on a dry surface.


Related Solutions

The number of hours 10 students spent studying for a test and their scores on that...
The number of hours 10 students spent studying for a test and their scores on that test is represented in the table below. Hours spent studying, x 0 2 4 5 5 5 6 7 8 9 Test scores, y 40 51 64 69 73 75 93 90 95 95 7) What amount of the variance in test score (y) do the hours spent studying (x) account for this sample? (r2 =?) Interpret the result in the context of the...
The number of hours 10 students spent studying for a test and their scores on that...
The number of hours 10 students spent studying for a test and their scores on that test is represented in the table below. Hours spent studying, x 0 2 4 5 5 5 6 7 8 9 Test scores, y 40 51 64 69 73 75 93 90 95 95 3) Describe the type of correlation and interpret the correlation in the context of the data. Be specific in describing the magnitude, direction, and strength of the relationship. (12p) 4)...
The number of hours 10 students spent studying for a test and their scores on that...
The number of hours 10 students spent studying for a test and their scores on that test are shown in the table. Is there enough evidence to conclude that there is a significant linear correlation between the​ data? Use alphaαequals= .01 X(hours) = top row; Y(score)=bottom row 0 1 2 3 4 4 5 6 7 8 41 46 52 50 65 68 75 85 82 91 Set up hypothesis test = ?? Critical Values = ?? Calculate test statistic;...
The number of hours 1010 students spent studying for a test and their scores on that...
The number of hours 1010 students spent studying for a test and their scores on that test are shown in the table. Is there enough evidence to conclude that there is a significant linear correlation between the​ data? Use alphaαequals=0.050.05. ​ Hours, x 00 11 22 44 44 55 55 66 77 88 Test​ score, y 4141 4040 5555 5656 6464 6666 7575 7878 8181 9797 LOADING... Click here to view a table of critical values for​ Student's t-distribution. Setup...
The following data gives the number of hours 10 students spent studying and their corresponding grades...
The following data gives the number of hours 10 students spent studying and their corresponding grades on their midterm exams. Hours Spent Studying 0 0.5 1 2 2.5 3 4 4.5 5 5.5 Midterm Grades 60 63 75 81 84 87 90 93 96 99 Determine if r is statistically significant at the 0.01 level.
The following data gives the number of hours 10 students spent studying and their corresponding grades...
The following data gives the number of hours 10 students spent studying and their corresponding grades on their midterm exams. Hours Spent Studying 0 0.5 1 2 2.5 3.5 4 5 5.5 6 Midterm Grades 63 72 75 78 81 84 87 90 93 96 Step 1 of 3: Draw a scatter plot of the given data Step 2 of 3: Estimate the correlation in words: positive, negative, no correlation. Step 3 of 3: Calculate the correlation coefficient, r. Round...
The following data give the number of hours 10 students spent studying and their corresponding grades...
The following data give the number of hours 10 students spent studying and their corresponding grades on their midterm exams. Hours Studying 0 0.5 1 1.5 3 3 3.5 4 4 5.5 Midterm Grades 63 63 67 69 71 72 73 73 81 89 A. Calculate the sum of squared errors (SSE). Use the values b0=61.3521 and b1=4.1338 for the calculations. Round your answer to three decimal places. B. Calculate the estimated variance of errors, s2e. Round your answer to...
The number of hours spent studying by students on a large campus in the week before...
The number of hours spent studying by students on a large campus in the week before the final exams follows a normal distribution with standard deviation of 8.4 hours. A random sample of these students is taken to estimate the population mean number of hours studying. a. How large a sample is needed to ensure that the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05? b. Without doing the...
The following data give the number of hours 10 students spent studying and their corresponding grades on their midterm exams
The following data give the number of hours 10 students spent studying and their corresponding grades on their midterm examsStep 1 of 5:Calculate the sum of squared errors (SSE). Use the values b0=58.4077b0=58.4077 and b1=6.6860b1=6.6860 for the calculations. Round your answer to three decimal places.Step 2 of 5:Calculate the estimated variance of errors, s2ese2. Round your answer to three decimal places.Step 3 of 5:Calculate the estimated variance of slope, s2b1sb12. Round your answer to three decimal places.Step 4 of 5:Construct...
The following data give the number of hours 5 students spent studying and their corresponding grades...
The following data give the number of hours 5 students spent studying and their corresponding grades on their midterm exams. Hours Studying 1 1 2 3 6 Midterm Grades 65 73 74 86 91 Step 1 of 5: Calculate the sum of squared errors (SSE). Use the values b0=65.9185 and b1=4.5698 for the calculations. Round your answer to three decimal places. Step 2 of 5: Calculate the estimated variance of errors, s^2e. Round your answer to three decimal places. Step...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT