Find the critical value for the indicated t test, level of significance a, and s
ID: 3267796 • Letter: F
Question
Find the critical value for the indicated t test, level of significance a, and sample size n. 1. Right tailed test a= 0.05, n=23 2. Left tailed test a= 0.10, n=20 Use a t test to test the claim about the population mean p at the given level of significance a using the given sample statistics. 3. Claim mu greaterthanorequalto 8000: alpha = 0.01 Sample statistics: sample mean = 7700, s = 450. n = 25 4. A used car dealer says that mean price of a 2008 Subaru Forester is $18,000. You suspect this claim is incorrect and find that a random sample of 15 similar vehicles has a mean price of $18,550 and a standard deviation of $1767. Is there enough evidence to reject the claim at alpha = 0.05Explanation / Answer
Solution:-
3)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: > 8000
Alternative hypothesis: < 8000
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 = 90
DF = n - 1 = 25 - 1
D.F = 24
t = (x - ) / SE
t = - 3.33
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 - 3.33. We use the t Distribution Calculator to find P(t < - 3.33) = 0.0014
Thus the P-value in this analysis is 0.0014.
Interpret results. Since the P-value (0.0014) is less than the significance level (0.01), we have to reject the null hypothesis.
From the above test we do have sufficient evidence in the favor of the claim > 8000.
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