Ie is believed that nationally cars are driven 15,000 miles per year on average
ID: 3316021 • Letter: I
Question
Ie is believed that nationally cars are driven 15,000 miles per year on average and a follow 11GXpts) is anormal distnbution. To rest if this is true to the Baton Rouge area a sample of 100) randomly seleted car owners were recuited to log their mileage for a period of one year. If the sample 12,500, s 2000 miles, can it be concluded that the national average applies to Baton Rouge? a. State the null and alternative bypothess b. Choose a value for c. State the value of the test statistic: d. State your conclusion it. In the example above. (5 pts) What is the probability of making a Type II Error if the true mean for Baton Rouge was 10,000 miles.Explanation / Answer
Solution:-
A)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: = 15000
Alternative hypothesis: 15000
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.
b) Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample z - test.
Analyze sample data. Using sample data, we compute the standard error (SE), z statistic test statistic (z).
SE = s / sqrt(n)
S.E = 200
c)
z = (x - ) / SE
z = - 12.5
where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.
Since we have a two-tailed test, the P-value is the probability that the z statistic less than -12.5 or greater than 12.5.
Thus, the P-value = less than 0.0001.
Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis.
d) It can be concluded that the national average applies to Baton roughe.
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