Suppose the National Transportation Safety Board (NTSB) wants to examine the saf

ID: 3059379 • Letter: S

Question

Suppose the National Transportation Safety Board (NTSB) wants to examine the safety of compact cars, midsize cars, and full-size cars. It collects a sample of ten for each of the treatments (cars types). Using the hypothetical data provided below, test whether the mean pressure applied to the driver’s head during a crash test is equal for each types of car. At the 0.05 significance level, can we conclude that there is a difference in the mean pressures between compact, midsize or full size cars.) (Enter all numeric values in 4 decimals unless otherwise noted.)

1) State the null and alternative hypotheses

H_0: (Click to select)_c=_m=_f_c_m_f_c_m=_f
H_a: (Click to select)At least one of _c,_m,and _f differs._c_m_f.

2) Specify the significance level =0.05
3) Select the test statistic: F

4) Determine the rule for deciding whether or not to reject H0
     P-value Rule:
     Reject H_0 if (Click to select)>=0.05==0.05<=0.05
    Critical Value Rule:
    Reject H0 in favor of Ha if (Click to select)F> FF= FF< F
    F =

5) Collect the sample data and calculate the value of the test statistic or p-value

Test statistic:

p-value

6) Decide whether to reject H0 by using the test statistic or p-value and the rejection rule

We (Click to select)rejectfail to reject the null hypothesis because (Click to select)test statistic is less than the critical valuetest statistic is greater than the critical valuep-value is greater than the significance level.

7) Interpret the statistical results in managerial terms and assess their practical importance

(Click to select)With 95% confidence we can conclude that at least one of the population mean pressures is greater for compact, midsize and full-size cars. At 95% confidence we cannot conclude that at least one of the population mean pressures differs for compact, midsize and full-size cars. With 95% confidence we can conclude that at least one of the population mean pressures differs for compact, midsize and full-size cars.

Calculate the 95% Tukey simultaneous confidence intervals. (4 decimals)

_c-_m

_c-_f

_m-_f

If you were to make a recommendation to a friend, which of the compact, midsize and full-size cars would you tell to avoid in terms of safety? (Click to select)Mid-size carsCompact carsFull-size cars

3) Using the output below answer the following questions:

a. What is the null and alternative hypotheses for the yellow highlighted cell above?
H_0: (Click to select)_c _m_c=_m_c _m
H_a: (Click to select)_c_m_c<_m_c>_m

b. Can we conclude at 99% confidence that the population mean pressure for compact and midsize differ?

(Click to select)YesNo, because the t-value is (Click to select)greaterlessequalunequal than the critical value . (2 decimals)

c. Is it appropriate to perform the post-hoc analysis? (Click to select)YesNo Why? (Click to select)Because we rejected the null hypothesis testing whether the population mean pressures for compact, mid-size, and full-cars differ. We can always perform post hoc analysisWe do not know.

Compact Midsize Fullsize 300 404 499 354 443 426 234 421 329 399 418 421 278 499 426 358 374 414 379 362 332 356 305 360 196 375 394 156 438 537

Explanation / Answer