1. A researcher is testing the claim that adults consume an average of at least 1.85 cups of coffee per day. A sample of 35 adults shows a sample mean of 1.75 cups per day with a sample standard deviation of 0.4 cups per day. Test the claim at a 5% level of significance. What is your conclusion?

2. A government Bureau claims that more than 50% of U.S. tax returns were filed electronically last year. A random sample of 150 tax returns for last year contained 80 that were filed electronically. Test the Bureau’s claim at a 5% level of significance. What is your conclusion? Report the p-value for this test.

3. A major automobile company claims that its New electric-powered car has an average range of more than 100 miles. A random sample of 40 new electric cars was selected to test the claim. Assume that the population standard deviation is 12 miles. A 5% level of significance will be used for the test.

    A) What would be the consequences of making a Type II error in this problem?

    B) Compute the Probability of making a Type II error if the true population mean is 105 miles.

    C) What is the maximum probability of making a Type I error in this problem?

Please Note: A hypothesis test answer must contain: a Null and an Alternate Hypothesis, a computed value of the test statistic, a critical value of the test statistic, a Decision, and a Conclusion.