correct At least one of the answers above is NOT correct. (1 point) It is necess
ID: 2936442 • Letter: C
Question
correct At least one of the answers above is NOT correct. (1 point) It is necessary for an automobile producer to estimate the number of miles per gallon (mpg) achieved by its cars. Suppose that the sample mean for a random sample of 50 cars is 29.5 mpg and assume the standard deviation is 3.4 mpg. Now suppose the car producer wants to test the hypothesis that the mean number of miles per gallon is not 28.8. Conduct a test using a significance level of 05 by giving the following: (a) The test statistic 1.455808 (b) The P-value 025 (c) The final conclusion is O A. There is enough evidence to support the claim. o B. There is not enough evidence to support the claim. Note: You can earn partial credit on this problem. Preview My Answers Submit Answers Your score was recorded.Your score was successfully sent to the LMSExplanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: = 28.8
Alternative hypothesis: 28.8
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.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = s / sqrt(n)
S.E = 0.481
DF = n - 1 = 50 - 1
D.F = 49
t = (x - ) / SE
t = 1.455
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 t statistic having 49 degrees of freedom is less than -1.46 or greater than 1.46
Thus, the P-value = 0.1442
Interpret results. Since the P-value (0.1442) is greater than the significance level (0.05), we cannot reject the null hypothesis.
There is not enough evidence to support the claim.
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