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Based on 2017 sales, the six top-selling compact cars are the Honda Civic, Toyota Corolla, Nissan Sentra, Hyundai Elantra, Chevrolet Cruze, and Ford Focus (New York Daily News). The 2017 market shares are Honda Civic 20%, Toyota Corolla 17%, Nissan Sentra 12%, Hyundai Elantra 10%, Chevrolet Cruze 10%, and Ford Focus 8%, with other small car models comprising the remaining 23%. A sample of 400 compact car sales in Chicago showed the following number of vehicles sold.
Honda Civic 98
Toyota corolla 72
Nissan Sentra 54
Hyundai Elantra 44
Chevrolet Cruze 42
Ford Focus 25
Others 65
Use a goodness of fit test to determine whether the sample data indicate that the market shares for cars in Chicago are different than the market shares suggested by nationwide 2017 sales. Using a 0.05 level of significance, what is the p-value?
The p-value is___________.
What is your conclusion?
Conclude that the markets shares for the five compact cars in Chicago _________the market shares reported. What market share differences, if any, exist in Chicago? Round your answers to three decimal places.

Sagot :

ogorwyne

Answer:

  • chi square good ness of fit = 14.99
  • p value = 0.00203
  • market share for the 5 compact cars differ from reported marketed shares
  • market share differences = 0.045, 0.01, 0.015, 0.01, 0.005, -0.0175, -0.0675

Step-by-step explanation:

1.

I made a table as seen in the first attachment to calculate the chisquare. from the calculations made the chisquare is given as:

X² = 4.05 + 0.235 + 0.75 + 0.4 + 0.1 + 1.531 + 7.924 = 14.99

to get the pvalue, i used the chi distribution function on excel.

n = 7

degrees of freedom = 7-1 = 6

α = 0.05

CHIDIST(14.99, 6) = 0.0020334635 = 0.00203

this pvalue lies between 0.01 and 0.025

conclusion

In conclusion, market share for 5 compact cars in Chicago differs from the market shares that was reported

2. market shares differences

= (sample market share - hypothesized share)

sample market share = observed/total

hypothesized share = given percentages

1. 98/400 = 0.245,

0.245-0.20 = 0.045

2. 72/400 = 0.18,

0.18 - 0.17 = 0.01

3. 54/400 = 0.135,

0.135 - 0.12 = 0.015

4. 44/400 = 0.11,

0.11 - 0.10 = 0.01

5. 42/400 = 0.105

0.105 - 0.10 = 0.005

6. 25/400 = 0.0625

0.0625-0.08 = -0.0175

7. 65/400 = 0.1625

0.1625 - 0.23 = -0.0675

View image ogorwyne
View image ogorwyne
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