Mktg 301

Topics: Probability theory, Variance, Random variable Pages: 15 (4364 words) Published: March 27, 2013
7) Data from a small bookstore are shown in the accompanying table. The manager wants to predict Sales from Number of Sales People Working. Number of sales people working| Sales (in $1000)|
4| 12|
5| 13|
8| 15|
10| 16|
12| 20|
12| 22|
14| 22|
16| 25|
18| 25|
20| 28|
x=11.9| y=19.8|
SD(x)=5.30| SD(y)=5.53|

a) Find the slope estimate, b1. Use technology or the formula below to find the slope. b1=rsysx
Enter x,y Data in TI-84 under STAT > STAT > CALC > 8: LinReg(a+bx) b1=1.023

b) What does b1 mean, in this context?
The slope tells how the response variable hanges for a one unit step in the predictor Thus, an additional; $1,023 of sales associated with each additional sales person working. c) Find the intercept, b0.

For this problem, use technology, rounding to three decimal places. b0=7.622
d) What does b0 mean in this contet? Is it meanful?
The intercept serves as a starting value for the predicitons. It shuld only be interpreted if a 0 value for the predictor variable makes sense for the context of the situation. On average, $7,622 is expected when 0 sales people are working. It is not meaningful because it does not make sense in this context. e) Write the equation that predicts Sales from Number of Sales People Working. Recall that the slope of the equation b1=1.023 and the intercept is b0=7.622 Complete the equation.

Sales=7.622+1.023 *(Number of Sales People Working)
f) If 19 people are working, what sales do you predict?
Substitute 19 for the number of sales people working in the equation found in the previous step and solve for Sales. Sales=7.622+1.023 *(Number of Sales People Working)
**Note that each unit of Sales represents $1000. Thus, the predicted sales for 19 people working is 27,059 dollars. g) If sales are actually $26,000, what is the value of the residual? Subtract the predicated value found in the previous step from the actual value. 26,000-27,059=-1059

Thus, the value of the residual is -1059 dollars.
h) Have the sale been overestimated or underestimated
The predicted sales are $27,059 and the actual sales are $26,000. Since $27,059 > $26,000, the sales were overestimated.

13) Of the 46 individuals who responded, 25 are concerned, and 21 are not concerned. 9 of those concerned about security are male and 5 of those not concerned are male. If a respondent is selected at random, find each of the fallowing conditional probabilities. | Male| Female| Total|

Concerned| 9| 16| 25|
Not Concerned| 5| 16| 21|
Total| 14| 32| 46|

a) The respondent is male, given that the respondent is not concerned about security. P(Male|Not Concerned) = 521 = 0.238 b) The respondent is not concerned about security, given that is female P(Not Concered|Female) = 1632 = 0.500

c) The respondent is female, given that the respondent is concerned about security. P(Female|Concerned) = 1625 = 0.640 14) It was found that 76% of the population were infected with a virus, 21% were without clean water, and 18% were infected and without clean water | Clean Water| |

| Yes| No| Total|
Infected| 0.58| 0.18| 0.76|
Not Infected| 0.21| 0.03| 0.24|
Total| 0.79| 0.21| 1.00|

a) What’s the probability that a surveyed person had clean water and was not infected? .21 had clean water and was not infected

15) A survey concluded that 54.4% of the households in a particular country have both a landline and a cell phone, 32.6% have only cell phone services but no landline, and 4.6% have no telephone services at all.

a) What proportion of households have a landline?
Begin by making a contingency table.
| Cell Phone| |
| Yes| No| Total|
Landline| 0.545| 0.083| 0.628|
No Landline| 0.326| 0.046| 0.372|
Total| 0.871| 0.129| 1.00|

The completed contingency tables shows that...
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