Use technology to help you test the claim about the population mean, mu , at the
ID: 3200909 • Letter: U
Question
Use technology to help you test the claim about the population mean, mu , at the given level of significance, alpha , using the given sample statistics. Assume the population is normally distributed. Claim: mu less than or 1170; alpha =0.07; sigma =204.48. Sample statistics: x overbar equals 1190.79, n= 275
Determine the P-value. P=___ (Round to three decimal places as needed.)
Determine the outcome and conclusion of the test.
(1) ____Upper H 0 . At the 7 % significance level, there (2)_____ enough evidence to (3)____ the claim.
(1) Reject/ Fail to reject
(2) is not/ is
(3) reject/ support
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: < 1170
Alternative hypothesis: > 1170
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).
sigma =204.48, x overbar equals 1190.79, n= 275
SE = s / sqrt(n)
S.E = 12.3329
DF = n - 1 = 275 - 1
D.F = 274
t = (x - ) / SE
t = 1.685
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.
Thus the P-value in this analysis is 0.04656
Interpret results. Since the P-value (0.04656) is less than the significance level (0.07), we have to reject the null hypothesis.
From the test can conclude that we do not have sufficient evidence in the favor of the claim that mu less than or 1170.
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