z-test for all: Z t-test for a : 1--,(s unknown) d\'sn-1 DY-25 z = P-p Pq /n z-t
ID: 3319954 • Letter: Z
Question
z-test for all: Z t-test for a : 1--,(s unknown) d'sn-1 DY-25 z = P-p Pq /n z-test for a P: Correlation coefficient: r y=mr+b -ry-Dx)(y) b,2-,2 Regression Line Equation: m Graphs are necessary! A hat company claims that the mean hat size for a male is at least 7.25. A random sample of 12 hat sizes has a mean of 7.15. At 0.01, can you reject the company's claim? Assume the population is normally distributed and the population standard deviation is 0.27 1. a.) Hypotheses: Ho: Ha: Level of Significance: = Sample Size: n b.) Calculate the test statistic: c.) Use P-value or Rejection Region: Draw a sketch that illustrates the relationship between the critical values in this situation. d.) Decision: e) Conclusion ofExplanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: > 7.25
Alternative hypothesis: < 7.25
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 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 = 0.07794
z = (x - ) / SE
z = - 1.28
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 - 1.28.
Thus the P-value in this analysis is 0.1003.
Interpret results. Since the P-value(0.1003) is greater than the significance level (0.01), we cannot reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that mean hat size for male is at least 7.25.
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