Statistics for Business and Economics chapter 10

We will reject the null hypothesis of “no increase” if the p­value ≤ .05.. For an upper tail hypothesis test, the p­value is the area in the upper tail at the value of the test statistic

d We will reject the null hypothesis of “no increase” if the p­value ≤ .05. For an upper tail hypothesis  test, the p­value is the area in the upper tail at the value of the test statistic. A value of z = 1.645 

e The increase from 2007 to 2008 for J.C. Penney is not statistically significant because it is less than 1.80.  We cannot conclude that customer service has improved for J.C. Penney

9 a x1 x2= 22.5 ­ 20.1 = 2.4

2.281

2

1.791

1.4310.1

c ( )2 26 2.08

i d

i d

i d

d d

x x

n



   hours per week for cable television

3002015

i R

x x

3.31621

i d

c      α= .05      df = 19 t = 1.729

Margin of error = .025 d

s t

n  = 1.7293.3162 1.28

20 Yes, just check to see if the 90% confidence interval includes a difference of zero. If it does, the difference is not statistically significant

.07  .0691 (.0009 to .1391)

7% more executives are predicting an increase in full­time jobs.  The confidence interval shows the difference may be from 0% to 14%

Upper tail p-value is the area to the right of the test statistic

Using normal table with z = 1.23: p-value = 1 - 8907 = 1093

p­value >    α; do not reject H0

We cannot conclude that women are more likely to ask directions

900 1200

p p z

d There is a statistically significant difference between the population proportions for the two age groups. The stronger appeal is with the younger, under 30, age group. Miller Lite is most likely pleased and encouraged by the results of the poll. "The Miller Lite Girls" ad ranked among the top three Super Bowl ads in advertising effectiveness. In addition, 49% of the younger, under 30, group liked the ad a lot. While a response of 36% for the older age group was not bad, Miller Lite 

probably liked, and probably expected, the higher rating among the younger audience. Since a younger audience contains the newer beer drinkers, appealing to the younger audience could bring new customers to the Miller Lite product. The older age group may be less likely to change from their established personal favorite beer because of the commercial

Note: In 1993, a round trip Newark to San Francisco was $388. In 2003, a special fare for the same trip was $238

39 a 1

1

6,776,900 225,89730

1

55, 2071

i

x x s

We are 99% confident that home prices have declined by between $21,973 and $87,835

c To answer this question we need to conduct a one-tailed hypothesis test No value for the level of

significance (α) has been given But, most people would agree that a p-value � 01 would justifyconcluding that prices have declined from 2006 to 2009

::

a

H H

We are 90% confident that the population mean price per share has decreased between $.30 and

$4.60 over the four month period

c Sample mean price per share January 1: 460.94 $30.73

15

i

x x n

�

Percentage decrease over the 4 months: 2.45 (100) 8%

d Mean price per share December 31, 2009 = $30.73(.92)(.92)(.92) = $23.93 This is a decline of

$30.73 – 23.93 = $6.80 per share for the year

43 a p1 = population proportion for men

p2 = population proportion for women

H0:   p1 ­ p2  =  0

.19(1 19) 10(1 10).19 10 1.96

z   

p­value = .0025

With p­value ≤ .01, we reject H0 and conclude that bullish sentiment has declined over the past month