Use the following set of points to test the null hypothesis H0: β1=0 versus H1: β1 ≠ 0. Use the critical value method with the α=0.05 level of significance. The slope of the regression line for this data is computed to be b1=-0.13834, and the standard error of b1 is computed to be sb=0.264048.
x | 15 | 17 | 3 | 22 | 12 | 10 |
---|---|---|---|---|---|---|
y | 8 | 16 | 17 | 16 | 17 | 17 |
Find the critical value(s). Round the answer to three decimal places. If there is more than one critical value, separate them with commas.
Critical value(s):
Use the following set of points to test the null hypothesis H0: β1=0
In a one-tailed t-test, the null hypothesis is H0: population β1≥0. If the test statistic = – 1.529, and the critical value you find from the t-table is 2.164, do you reject the null hypothesis?
6. (4 points) Suppose n = 82. How much is σˆ 2 , the estimated variance of the error term ui? A. 0.00625 B. 0.0125 C. 0.025 D. 0.05 7. (4 points) Suppose βˆ 1 = 0.75, SE(βˆ 1) = 0.01 and n = 52. Then the 90% confidence interval for βˆ 1 would be A. [0.4224, 1.1994] B. [0.6112, 0.9112] C. [0.7336, 0.7664] D. [0.7229, 0.7661] 8. (4 points) Suppose one tested and rejected the null hypothesis H0 :...
Suppose we do not reject the t-test null hypothesis of H0: β1 = 0 for a regression. In this case, we think there is evidence that the X variable values help explain the Y variable values. True or False
Q. 20 In a simple linear regression, when testing H0: β1 = 0, against H1: β1 ≠0, failing to reject the null hypothesis means that: a. the slope of the regression line is not zero b. the relationship between x and y may be multiplicative c. there is no linear relationship between x and y d. there is a linear relationship between x and y e. None of the above
I need help with - d) Assuming the residuals are normally distributed, test Ho : β1=0 versus H1 : β1 ≠ 0 at the α = 0.05 level of significance - at the bottom of the page. Thank you! For the data set shown below. x y 20 98 30 95 40 89 50 85 60 72 (a) Use technology to find the estimates of β0 and β1. β0 ≈ b0= 112.6 (Round to two decimal places as needed.) β1...
1) Suppose that you are interested in the relationship between the return rate on a stock in 2010 compared to the return rate in 2009. You believe that the return rates in both years are positively correlated. A sample of 15 stocks yields the following regression results: b0= 5.3, b1= 1.04, s= 1.79, s = 0.2163, R2 = 0.64, and MSE = 35.4. Calculate the regression sum of squares. What is the correlation coefficient for the stock returns of the...
A researcher poses a null hypothesis of H0: µ1 ≤ µ2, and a research hypothesis of H1: µ1 > µ2. The researcher selects an α = 0.05 critical threshold. The test has 11 degrees of freedom. The researcher obtains a t-statistic of 1.67. Determine which course of action is most appropriate. Reject the null hypothesis. Do not reject the null hypothesis. Cannot determine with the information given.
#1 part A.) To test H0: μ=100 versus H1: μ≠100, a random sample of size n=20 is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below. (aa.) If x̅=104.4 and s=9.4, compute the test statistic. t0 = __________ (bb.) If the researcher decides to test this hypothesis at the α=0.01 level of significance, determine the critical value(s). Although technology or a t-distribution table can be used to find the critical value, in...
A researcher poses a null hypothesis of H0: µ1 ≤ µ2, and a research hypothesis of H1: µ1 > µ2. The researcher selects an α = 0.05 critical threshold. The test has 11 degrees of freedom. The researcher obtains a t-statistic of 1.67. Determine which course of action is most appropriate.
3) Use critical values to test the null hypothesis H0: μ1 − μ2 = 20 versus the alternative hypothesis Ha: μ1 − μ2 ≠ 20 by setting α equal to .05. How much evidence is there that the difference between μ1 and μ2 is not equal to 20?