The average amount spent on a new car in 2015 was $33,560 with a standard deviat
ID: 3319963 • Letter: T
Question
The average amount spent on a new car in 2015 was $33,560 with a standard deviation of $11,194. You just bought a new car for $18,422 and want to know if you got a good deal compared to the national average. (Total 25 pts)
A. What are the independent and dependent variables and how are each scaled (1 pt each; Total 4 pts)?
Independent:________________________ Scaling:_____________________________
Dependent:__________________________ Scaling:_____________________________
B. What test should you use (4 pts)?__________________________________________________
C. Why that test (2 pts)?
D. What are the null and alternative hypotheses for that test (4 pts)?
E. What are that tests assumptions (2 pts)?
F. What is the critical value for p=.05 (2 pts)? _________________________
G. If you calculate a test statistic of 1.97, should she (2 pts)? Retain H0 Reject H0 H. Interpret the findings (5 pts):
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: > 33,560
Alternative hypothesis: < 33,560
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.
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 = 11194
z = (x - ) / SE
z = - 1.35
zcritical = - 1.645
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.
The observed sample mean produced a z statistic test statistic of - 1.35.
Thus the P-value in this analysis is 0.0885.
Interpret results. Since the P-value (0.0885) is greater than the significance level (0.05), we cannot reject the null hypothesis.
G. If you calculate a test statistic of 1.97, she should Retain H0.
Retaining H0, means that she does'nt got a good deal compared to the national average.
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