Am I on the right track? Stuck here STAT-4013 Statistical Methods I Example: A c
ID: 3315747 • Letter: A
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Am I on the right track? Stuck here STAT-4013 Statistical Methods I Example: A consumer-testing agency wants to evaluate the claim made of discount tires. The manufacturer claims that its tires can be driven a Chapter 5 Lecture Notes (5.7 One-Sample Inferenc by a manufacture t least 35,000 mile maucg out. T'o determine the average number of miles that can be obtained from t manufacturer's tires, the agency randomly selects 25 tires from the manu warehouse and places the tires on machines meant to simulate wear and tear while driving tires is 31.47 thousand miles and the standar The mean number of miles for the fiftcn eviation was 5.04-thousand miles. Is there significant evidence (a anufacturer's claim is false? n-25 5, 04x103 M 235,oo Ho MF 35,000 31470 35,000 5040 2. 5 ~-3.50198 df:H .s1,2t-2.ta2 CV:o/s,01 PC 2492-3.502) eect HoExplanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: > 35,000
Alternative hypothesis: < 35,000
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 0.01. 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 = 1008
DF = n - 1
D.F = 24
t = (x - ) / SE
t = - 3.50
tcritical = - 2.492
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 t statistic test statistic of - 3.50. We use the t Distribution Calculator to find P(t < - 3.50).
Thus the P-value in this analysis is 0.00092.
Interpret results. Since the P-value (0.00092) is less than the significance level (0.01), we have to reject the null hypothesis.
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