1. The Heldrich Center for Workforce Department found that 45% of Internet users received more than 10 email messages per day. Recently, a similar study on the use of email was reported. The purpose of the study was to see whether the use of email increased.
a. Formulate the null and alterative hypotheses to determine whether an increase occurred in the proportion of Internet users receiving more than 10 email messages per day.
b. If a sample of 420 Internet users found 208 receiving more than 10 email messages per day, what is the p-value?
c. Using α =.05, what is your conclusion?
d. Apply the critical value method when a = .01.
2. A mail-order business prides itself in its ability to fill customers' orders in less than six calendar days, on average. Periodically, the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders. On one occasion when a sample of 39 orders was selected, the average number of days was 6.65 with a population standard deviation of 1.5 days. Apply the p-value and the critical value approaches to test the hypotheses at a significance level α =.10.
3. The manufacturer of an over-the-counter heartburn relief mediation claims that it product brings relief in less than 3.5 minutes, on average. To be able to make this claim the manufacturer was required by the FDA to present statistical evidence in support of the claim. The manufacturer reported that for a sample of 50 heartburn sufferers, the mean time to relief was 3.3 minutes and the population standard deviation was 1.1 minutes. Test the hypotheses at a significance level α =.05 using the critical value approach.