150021.SC . A random sample of 100 observations was selected from a population w

Question

150021.SC . A random sample of 100 observations was selected from a population with mean of .04. Hint; use a standard deviation of 60 vielded a sample mean of 110. (a) Test that the the population is larger than 100 using significance level of normal distribution. Thre e kind of hypothesis and sketch the corresponding areas. (e) Also, find the 76% confidence interval of the true mean. Sketch the corresponding diagram! Note: Use the five-step hypothesis testing procecdure to solve the following exercises (25 points)

Explanation / Answer

Solution:-

a)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: < 100
Alternative hypothesis: > 100

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 0.04. 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 = 6

z = (x - ) / SE

z = 1.67

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 1.67.

Thus the P-value in this analysis is 0.0475

Interpret results. Since the P-value (0.0475) is greater than the significance level (0.04), we have to accept the null hypothesis.

c) 76% confidence interval for the mean is C.I = (102.95, 117.05)

C.I = xbar + zalpha/2 × S.E

C.I = 110 + 1.175 × 6

C.I = 110 + 7.05

C.I = (102.95, 117.05)

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