Studyguidev Part4 Solutions Hyptestandreg 1

Solutions to Questions on Hypothesis Testing and Regression
1. A mileage test is conducted for a new car model, the “Pizzazz.” Thirty (n=30) random selected Pizzazzes are driven for a month and the mileage is carefully measured in each.
The mean mileage for the sample is 28.6 miles per gallon (mpg) and the sample standard deviation is 2.2 mpg. Estimate a 95% confidence interval for the mean mpg in the entire population of Pizzazzes (you might need to round your answer a little bit to agree with mine). (a)
(b)
(c)
(d)
(e)

(23.42, 33.84)
(27.81, 29.39)
(26.82, 30.47)
(27.23, 30.03)
None of the above

2. Determine the test statistic for testing the null hypothesis that the population mean is 27 mpg ( H0 : µ = 27 Ha : µ ≠ 27 )
(a)
(b)
(c)
(d)
(e)
(f)

t = 3.98 t = -3.98 t = 4.6 t = -4.6 t = 1.96
None of the above

3. A Type II error is made when
a.
b.
c.
d.
e.

the null hypothesis is accepted when it is false. the null hypothesis is rejected when it is true. the alternate hypothesis is accepted when it is false. the null hypothesis is accepted when it is true. the alternate hypothesis is accepted when it is true.

4. A recent USA TODAY/CNN/Gallup Poll showed that most American people support
Bush’s efforts in the Middle East peace process. The poll of 2000 adults was conducted and 1243 people said they supported Bush’s efforts.
a) Find a 95% confidence interval for p, the fraction of Americans who support Bush’s efforts phat = 1243/2000 =62.15% then use the CI formula for a proportion
b) Perform the hypothesis test Ho : p = 0.6 versus Ha : p > 0.6.

pˆ = 62.15% t= .6215 −.60
(.6)(.4) / 2000

= 1.52

We reject the null hypothesis if T > 1.64 and since its not, we fail to reject the null hypothesis. 5. A random sample of 100 voters in a community produced 59 voters in favor of candidate
A. The observed value of the test statistic for testing the null hypothesis Ho : p = 0.5 versus the alternative hypothesis Ha : p ≠ 0.5 is:
a) 1.80
b) 1.90
c) 1.83
d) 1.28
e) 1.75
6.