Question

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 1.70 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 86 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 50 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 means 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.

Answer 1

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 1.70 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?

Answer)

Null hypothesis Ho : u >= 1.85

Alternate hypothesis Ha : u < 1.85

As the population s.d is unknown here, we will use t distribution to estimate the test

Test statistics t = (sample mean - claimed mean)/(s.d/√n)

t = (1.7 - 1.85)/(0.4/√35) = -2.219

Degrees of freedom is = n-1 = 34

For 34 df and -2.219 test statistics

P-value from t distribution is = 0.0166

As obtained P-value is less than 0.05 (5%) given significance level

We reject the null hypothesis that u >=1.85

So we do not have enough evidence to support the claim that adults consume an average of at least 1.85 cups of coffee per day.