Question
In: Statistics and Probability
CAR 1 MILEAGE CAR 2 MILEAGE CAR 3 MILEAGE CAR 4 MILEAGE 1 14.9 2 10.8...
| CAR 1 | MILEAGE | CAR 2 | MILEAGE | CAR 3 | MILEAGE | CAR 4 | MILEAGE |
| 1 | 14.9 | 2 | 10.8 | 3 | 19 | 4 | 18.9 |
| 1 | 17.7 | 2 | 10.7 | 3 | 13.8 | 4 | 19.2 |
| 1 | 17.7 | 2 | 11 | 3 | 20.1 | 4 | 19.4 |
| 1 | 18.7 | 2 | 12 | 3 | 19.8 | 4 | 21 |
| 1 | 19.8 | 2 | 7.5 | 3 | 12.2 | 4 | 13.5 |
| 1 | 21.1 | 2 | 10.5 | 3 | 24.3 | 4 | 17.2 |
| 1 | 17.3 | 2 | 9.1 | 3 | 21.8 | 4 | 12.7 |
| 1 | 19.8 | 2 | 10.7 | 3 | 20.7 | ||
| 1 | 16.3 | 2 | 7.5 | 3 | 16.4 | ||
| 1 | 17.8 | 2 | 12.1 | 3 | 25.4 |
With the above data, could you please help me answer the questions below.
| 10. What was the margin of error for the confidence interval for gasoline mileage of make 2? | |
| 11. What was the lower 95% confidence limit for make 2 mileage? | |
| 12. What was the upper 95% confidence limit for make 2 mileage? | |
| 13. What is the value of the t test statistic for testing the hypothesis that makes 2 and 3 do not differ in mileage? |
Solutions
Expert Solution
- Margin of error = Critical value x Standard deviation for the population.
- Margin of error = Critical value x Standard error of the sample
Here, complete table is:
| A | B | C | D | E | F | G | H | I | |
| CAR 1 | MILEAGE | CAR 2 | MILEAGE | CAR 3 | MILEAGE | CAR 4 | MILEAGE | ||
| 1 | 14.9 | 2 | 10.8 | 3 | 19 | 4 | 18.9 | ||
| 1 | 17.7 | 2 | 10.7 | 3 | 13.8 | 4 | 19.2 | ||
| 1 | 17.7 | 2 | 11 | 3 | 20.1 | 4 | 19.4 | ||
| 1 | 18.7 | 2 | 12 | 3 | 19.8 | 4 | 21 | ||
| 1 | 19.8 | 2 | 7.5 | 3 | 12.2 | 4 | 13.5 | ||
| 1 | 21.1 | 2 | 10.5 | 3 | 24.3 | 4 | 17.2 | ||
| 1 | 17.3 | 2 | 9.1 | 3 | 21.8 | 4 | 12.7 | ||
| 1 | 19.8 | 2 | 10.7 | 3 | 20.7 | ||||
| 1 | 16.3 | 2 | 7.5 | 3 | 16.4 | ||||
| 1 | 17.8 | 2 | 12.1 | 3 | 25.4 | ||||
| Formula in Excel | |||||||||
| Mean | xbar | 18.11 | 10.19 | AVERAGE(E2:E11) | 19.35 | 17.414 | |||
| Stdev | s | 1.81564191 | 1.6408 | STDEV(E2:E11) | 4.2222 | 3.1567 | |||
| count | n | 10 | 10 | COUNT(E2:E11) | 10 | 7 | |||
| alpha | 0.05 | ||||||||
| margin of error | |||||||||
| critical value | t | 2.26215716 | ABS(TINV(0.05,9)) | ||||||
| sigma | sigmahat | 1.6407654 | |||||||
| root n | 3.16227766 | ||||||||
| 1.17373286 | |||||||||
| t-test | 3.9206E-05 | TTEST(E2:E11,H2:H11,2,3) | |||||||
| rounded p-value | 0 |
10. margin of error for the confidence interval for gasoline mileage of make 2 is
Thus,
Margin of error for make 2= 1.173733
11. lower 95% confidence limit for make 2 mileage
12. upper 95% confidence limit for make 2 mileage
where,
13. value of the t test statistic for testing the hypothesis that makes 2 and 3 do not differ in mileage?
- Null hypothesis-H0: difference=d=mu2-mu3=0 [No significant change]
- Alternative-H1: mu2-mu3 not equal to zero
t-test statistic,
where, Xbar and Ybar are means of make 2 gasoline mileage and make 3 mileage respectively.
orchestra answered 1 year agoRelated Solutions
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