Now look at the variable DIFFERENCE (Since we do not know the population standard deviation σ, you have to use the sample standard deviation s as an estimate of σ). If there is no difference between the computer-calculated and driver-calculated mpg, then the average DIFFERENCE should be zero. Do the hypothesis testing (test significance) step-by-step by filling out the values in the diagrams below. Population: X = The Difference (Computer – Driver) mpg X ~ population distribution unknown (not normal) μ = E(X) = avg. DIFFERENCE in calculated mpg = ??? σ = σ(X) = std. dev. of the difference = ??? Hypotheses: H0 : ? = ?? = 0 vs. Ha : ? ≠ 0 (Circle one) This is a(n) a. upper-sided test b. lower-sided test c. two-sided test Significance Level: ? = 0.05 Sample: n = 20 DATA (from RStudio output): ?̅ = 2.73 (Statistic) s = 2.8015 (Statistic) ?̅ ~ ??? ??̅ = ? = ??? t = ?̅ − ? ??̅ ~ ??−?(t-distribution with df = n-1) df = n – 1 = 19 Standard Error: ??̅ = s/√? = _________________ ASSUME H0 IS TRUE: ??̅ = ?? = 0 Test Statistic: t =_______________ p-value = P ( T > | t | ) = 2 × _________________ Use t-Table to get an approximate p-value. Note: the two-sided p-value is twice (two times) the one-sided p-value.
Now look at the variable DIFFERENCE (Since we do not know the population standard deviation σ, you have to use the sample standard deviation s as an estimate of σ). If there is no difference between the computer-calculated and driver-calculated mpg, then the average DIFFERENCE should be zero. Do the hypothesis testing (test significance) step-by-step by filling out the values in the diagrams below.
Population:
X = The Difference (Computer – Driver) mpg
X ~ population distribution unknown (not normal)
μ = E(X) = avg. DIFFERENCE in calculated mpg = ???
σ = σ(X) = std. dev. of the difference = ???
Hypotheses: H0 : ? = ?? = 0 vs. Ha : ? ≠ 0
(Circle one) This is a(n)
a. upper-sided test
b. lower-sided test
c. two-sided test
Significance Level: ? = 0.05
Sample: n = 20 DATA (from RStudio output):
?̅ = 2.73 (Statistic) s = 2.8015 (Statistic)
?̅ ~ ??? ??̅ = ? = ???
t = ?̅ − ? ??̅ ~ ??−?(t-distribution with df = n-1) df = n – 1 = 19
Standard Error: ??̅ = s/√? = _________________
ASSUME H0 IS TRUE: ??̅ = ?? = 0 Test Statistic: t =_______________ p-value = P ( T > | t | ) = 2 × _________________
Use t-Table to get an approximate p-value.
Note: the two-sided p-value is twice (two times) the one-sided p-value.
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