car company wants to know the monthly sales made in ($000), based on the brand of vehicle. The data collected was entered on a MINITAB spreadsheet for analysis. Exhibit II below was subsequently generated. Exhibit 2 Model N Mean Median Tri Mean STD Dev SE Mean Hyundai 23 109 135 107.64 * 1.34 Toyota 27 165 124 143.65 9.5 ** d) Assuming normality, construct and interpret a 90% confidence interval for the average monthly earning from Toyota Vehicles. e) You are required to test at the 5% level of significance the hypothesis that the average monthly earnings on Hyundai Vehicles is equal to $110,000 versus the alternative that it is different from $110,000. Complete the following: i. Give the null and alternative hypothesis of this test. ii. Determine the critical value(s) of this test. iii. Compute the value of the test statistic. iv. State the decision rule. v. Give your decision based on the available sample evidence. vi. Hence, state your conclusion.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
A car company wants to know the monthly sales made in ($000), based on the brand of vehicle. The data collected was entered on a MINITAB spreadsheet for analysis. Exhibit II below was subsequently generated.
Exhibit 2
| Model | N | Mean | Tri Mean | STD Dev | SE Mean | |
| Hyundai | 23 | 109 | 135 | 107.64 | * | 1.34 |
| Toyota | 27 | 165 | 124 | 143.65 | 9.5 | ** |
d) Assuming normality, construct and interpret a 90% confidence interval for the average monthly earning from Toyota Vehicles.
e) You are required to test at the 5% level of significance the hypothesis that the average monthly earnings on Hyundai Vehicles is equal to $110,000 versus the alternative that it is different from $110,000.
Complete the following:
i. Give the null and alternative hypothesis of this test.
ii. Determine the critical value(s) of this test.
iii. Compute the value of the test statistic.
iv. State the decision rule.
v. Give your decision based on the available sample evidence.
vi. Hence, state your conclusion.
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