When testing the claim H_0: rho = 0 for 10 pairs of (x, y)data, the Pearson corr

Question

When testing the claim H_0: rho = 0 for 10 pairs of (x, y)data, the Pearson correlation coefficient test statistic is r = 0.68. Find the critical values of for this test, and state the decision and conclusion of this test at a significance level of 0.01. The sample is too small for conclusion the 0.01 level. Reject H_0: rho =0, and conclude that there is no linear correlation. Reject H_0: rho = 0, and conclude that there is linear correlation. Fail to reject H_0: rho = 0, and conclude that there is no linear correlation Fail to reject H_0: rho = 0, and conclude that there is linear correlation. The coefficient of determination, r^2, is a measure of: skew. the amount of variation in the y-variable that is explained by the regression of line. the location of regression line. the spread of the predicted values. A veterinarian collected a random sample of pairs of data consisting of heights (x) and weights(y) of Chihuahuas. She computed the test statistic this data to be r = 0.444, the mean height (x bar)to be 7.90 inches the mean weight (y bar) to be 5.30 pounds, and the regression equation to be y = 0.84x +1.60. If the critical values for this data are r = plusminus 0.532, find the best predicted weight (in pounds) for a that is 5.5 inches tall. 8.24 6.22 7.90 5.30 None of these A college tested for linear correlation between its statistics students' attitude ratings (x) and grades (y) by using a random sample of 25 students. In this test, the significance level was alpha = 0.05, the test statistic was r = 0.401, the regression equation was y circ = 11.7+1.02x, the mean attitude rating (x bar) was 62.1, and the mean grade (y bar) was 75.3. Find the best predicted grade for a student whose attitude is 63. 75.0 76.0 62.1 75.3 None of these

Explanation / Answer

SOL:

We follow standard hypothesis test procedures in conducting a hypothesis test for the population correlation coefficient . First, we specify the null and alternative hypotheses:

Null hypothesis H0: = 0
Alternative hypothesis HA: 0

alpha=0.01

r=0.68

n=10

The P-Value is 0.030501. The result is not significant at p < 0.01.

fail to reject null hypothesis

NO LINEAR RELATION

ANSWER D

SOLUTION78

Y HAT=0.84X+1.60

X=5.5

SUBSTITUTE TO GET THE ANS

Y HAT=0.84(5.5)+1.60

=6.22

ANSWER B

sOLUTION79

Y HAT=11.7+1.02X

X=63

Y HAT=11.7+1.02(63)

=75.96

=76

(ROUND TO NEAREST INTEGER)

ANSWER B

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