In: Statistics and Probability
You are testing the null hypothesis that there is no linear relationship between two variables, X and Y. From your sample of n =18, you determine that b1=4.2 and Sb1equals=1.2
a. What is the value of tSTAT?
b. At the alphaα=0.05 level of significance, what are the critical values?
c. Based on your answers to (a) and (b), what statistical decision should you make?
d. Construct a 95% confidence interval estimate of the population slope, betaβ1.
Slope hypothesis test
Ho: ß = 0
Ha: ß ╪ 0
n = 18
alpha,α = 0.05
estimated slope= 4.2
std error = 1.2
t-test statistic = t = estimated slope / std
error = 4.2 / 1.2
= 3.500
Df = n - 2 = 16
critical t-value = +- 2.1199 [excel function:
=t.inv.2t(α,df) ]
since, | t-statistic | > | t critical value| ,
reject Ho
...............
confidence interval for slope
n = 18
alpha,α = 0.05
estimated slope= 4.2
std error = 1.2
Df = n-2 = 16
t critical value = 2.1199 [excel function:
=t.inv.2t(α,df) ]
margin of error ,E = t*std error = 2.1199
* 1.2 =
2.5439
95% confidence interval is ß1 ± E
lower bound = estimated slope - margin of error =
4.2 - 2.5439 =
1.6561
upper bound = estimated slope + margin of error =
4.2 + 2.5439 =
6.7439
...................
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