DHW10.pdf d .> Apps Introduction to ElectWatch Kansas City Ch HW10.pdf Secure ht

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DHW10.pdf d .> Apps Introduction to ElectWatch Kansas City Ch HW10.pdf Secure https://learn.wsu .edu/bbcswebdav/pid-2291123-dt-content-rid-35833273 1/courses/2017-FALL-PULLM-STAT-360-1740-LEC/Hw10.pdf 1. A new design for the braking system on a certain type of car has been proposed. For the current system, the true average braking distance at 40 mph under specified conditions is known to be 120 ft. It is proposed that the new design be implemented only if sample data strongly indicates a reduction in true average braking distance for the new design. The summary statistics and the qq-plot is given below mean sd IQR 0% 25% 50% 75% 115.0633 5.1679 6.675 101.7 111.6 115.15 118.275 100% n 123.4 30 Carry out a hypothesis test to decide whether the new design should be implemented. Use significance level of 0.05. (Follow the 4-step procedure for full credits.) (8pts) Verify if the test you use is appropriate. (2pts) A. B. 12-58 PM Type here to search 127/2017

Explanation / Answer

Question 1

Part A

Here, we have to use one sample t test for population mean.

The null and alternative hypothesis for this test is given as below:

H0: µ = 120 versus Ha: µ < 120

We assume = 0.05

We are given

Xbar = 115.0633

S = 5.1679

n = 30

df = n – 1 = 30 – 1 = 29

Lower critical value = -1.6991 (by using t-table or excel)

Test statistic formula is given as below:

t = (Xbar - µ) / [S/sqrt(n)]

t = (115.0633 – 120) / [5.1679 / sqrt(30)]

t = -4.9367/0.9435

t = -5.2322

P-value = 0.0000 (by using t-table)

= 0.05

P-value < = 0.05

So, we reject the null hypothesis H0 that average braking distance is 120 ft.

There is sufficient evidence to conclude that average braking distance is less than 120 ft.

New design should be implemented.

Part B

We have to check above test by using excel. Excel output for this test is given as below:

t Test for Hypothesis of the Mean

Data

Null Hypothesis m=

120

Level of Significance

0.05

Sample Size

Sample Mean

115.0633

Sample Standard Deviation

5.1679

Intermediate Calculations

Standard Error of the Mean

0.9435

Degrees of Freedom

t Test Statistic

-5.2322

Lower-Tail Test

Lower Critical Value

-1.6991

p-Value

0.0000

Reject the null hypothesis

We get same results as per above.