QUESTION 22 and Park two cars having very different wheel bases and tuming ouete
ID: 3228805 • Letter: Q
Question
QUESTION 22 and Park two cars having very different wheel bases and tuming ouete onr 21 and 22 are d on the following An article in the wournal. "Human Factors" reports a study in which 10 subjects were asked to parallel parking and seconds longer rada The time to park car in din, waa rec d and is shown in the table below The researchers h that the average difference between 4 odr longer to park Car l) Set up the null and alternative hypotheses What is the p-value for the appropnate hypothesis test?Explanation / Answer
Solution:-
Given data -
Car 1 - 37,58,34,36,26,24,34,21,44,33
Mean 1 = 34.7
Standard deviation 1 = 10.64
Car 2 - 31,46,30,38,21,24,35,26,41,25
Mean 2 = 31.7
Standard deviation 2 = 8.14
The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. We work through those steps below:
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1 - 2 >= 4
Alternative hypothesis: 1 - 2 < 4
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the mean difference between sample means is too small.
Formulate an analysis plan. For this analysis, the significance level assumed is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = sqrt[(10.642/10) + (8.142/10)] =
DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] }
DF = (10.642/10 + 8.142/10)2 / { [ (10.642 / 10)2 / (9) ] + [ (8.142 / 10)2 / (9) ] }
DF = 322.092 / (14.24 + 4.878 ) = 16.85
t = [ (x1 - x2) - d ] / SE = [(34.7 - 31.7) - 4] / 4.472 = -0.224
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
Here is the logic of the analysis: Given the alternative hypothesis (1 - 2 < 4), we want to know whether the observed difference in sample means is small enough (i.e., sufficiently less than 4) to cause us to reject the null hypothesis.
We use the t Distribution Calculator to find P(t < -0.224) = 0.456
Therefore, the P-value in this analysis is 0.456.
Interpret results. Since the P-value (0.456) is greater than the significance level (0.05), we cannot reject the null hypothesis.
(A) The average time to park car 1 takes more than 4 seconds longer than to car 2.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.