1) Construct a 95% confidence interval estimate for the population mean given that s =30 , __ x = 45 and n = 20.
1) Construct a 95% confidence
2) A random sample of 81 workers at a company showed that they work an average of 100 hours per month with a standard deviation of 27 hours. At 95% confidence, how many more workers need to be included in the sample to provide a confidence interval with length 4 (i.e., the margin of error being 2)?
3) Given the following null and alternative hypothesis test: H0: µ ≥ 210 HA: µ < 210 If α = 0.025 with n = 25, s = 9, and x = 208.2, then
a. state the decision rule in terms of the critical value of test statistic.
b. calculate the value of the test statistic.
c. state the conclusion.
4) In the following null and alternative hypotheses H0 : =68 and H A : 68 , = 0.02 , x = 69.02 , = 5.4 and n = 40
a. State the decision rule in terms of the critical value of the test statistic.
b. State the calculated value of the test statistic.
c. State the conclusion. d. Compute the p-value. Does its value support the claim obtained in part a justify?
5) A company claims that the coffee contents in a bottle of coffee are at least 200 grams. To test their claim, a random sample of 20 bottles was taken and it was found that the mean contents in the sample were 190 grams with a sample standard deviation of 5 grams. At 0.01 level of significance, test H0: µ ≥ 200 against the alternative hypothesis HA: µ < 200. Can we conclude that the company’s claim is justified?
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