Q. 83 83. Using the data from Lap 1 on... [FREE SOLUTION]

91影视

Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset 91影视 Explanations$ Math

OER 2018 Edition 路 902 pages

ISBN: 9781938168208

Chapter 10: Q. 83 (page 601)

83. Using the data from Lap 1 only, conduct a hypothesis test to determine if the mean time for completing a lap in races is the same as it is in practices.

Short Answer

Expert verified

(a) The null hypothesis: $H_{0} : 渭_{1} = 渭_{2}$

(b) The alternate hypothesis: $H_{a} : 渭_{1} 鈮� 渭_{2}$
(c) The difference between the mean times for completing a lap in races and practice is denoted by ${\overset{炉}{X}}_{1} - {\overset{炉}{X}}_{2}$ .
(d) Student's t distribution : $t_{20.32}$
(e) The test statistic: $- 4.70$
(f) The $p$ -value: $0.0001$
(g) Check student's solution:

(h)(i) Alpha: $0.05$
(ii) Decision: Reject the null hypothesis.
(iii) Reason for Decision: $p$ -value $<$ alpha
(iv) Conclusion: There is sufficient evidence to conclude that the mean time for completing a lap in races is different from that in practices, at the $5 %$ significance level,

Step by step solution

Given information

To conduct a hypothesis test to determine if the mean time for completing a lap in races is the same as it is in practices by using the data from Lap 1 only.

Explanation

(a) The null hypothesis is defined as follows:
$H_{0} : 渭_{1} = 渭_{2}$
(b) The alternate hypothesis is defined as follows:
$H_{a} : 渭_{1} 鈮� 渭_{2}$
(c) The difference between the mean times for completing a lap in races and practice is denoted by $\overset{炉}{X_{1}} - \overset{炉}{X_{2}}$ .
(d) Student's t distribution is $t_{20.32}$ .
(e) For the mean difference, the paired test static as follows:

After ENTER all of the values, the OUTPUT will look like this:

Hence, the test statistic as: $- 4.70$ .

Explanation

(f) The $p$ -value from the output is $0.0001$

(g) Using the data from the last exercise, create a mental picture of the situation.
The horizontal axis should be clearly labelled and scaled, and the $p$ -value-corresponding region(s) on the graph should be shaded.

(h)

(i) $伪 = 0.05$

(ii) Decision: Null hypothesis is rejected.

(iii) $伪 > p$ -value

(iv) Conclusion: There is sufficient evidence to conclude that the mean time for completing a lap in races is different from that in practices at the $5 %$ significance level.