For questions 1 and 2, use confidence intervals to test the hypothesis. SHOW YOUR WORK including the null and alternative hypotheses. Write a conclusion in the following format: The z-score (include the #) is inside/outside of the confidence interval (include the interval) which means that we must reject/fail to reject the null hypothesis and conclude that (refer back to the stated purpose of the hypothesis test) .
1) A light bulb producing company states that its lights will last an average of 1200 hours with a standard deviation of 200 hours. A sample of 100 light bulbs from the company were tested and the researcher found that the average life of each light bulb was 1050 hours. At a 95% confidence level, determine whether these light bulbs are in compliance with the company's claim.
2) A company's human resource department claims that all employees are present on the average 4 days out of the work week with a standard deviation of 1. They hired an outside company to do an audit of their employees' absences. The company took a sample a 10 people and found that on the average the employees were present 3 days per week. With a 95% confidence level, determine whether the company's claim is true based on the data from the sample.
For questions 3-5 use the chi-squared distribution to test the hypothesis. SHOW YOUR WORK including the null and alternative hypotheses. Write a conclusion in the following format: Since the chi-square calculated from the data (include the #) is less than/greater than the p-value (include the #), we must reject/fail to reject the null hypothesis and conclude that (refer back to the stated purpose of the hypothesis test) .
3) A restaurant owner wants to see if the business is good enough for him to purchase a restaurant. He asks the present owner for a breakdown of how many customers that come in for lunch each day and the results are as follows: Monday - 20, Tuesday - 30, Wednesday - 25, Thursday - 40 and Friday - 55. The prospective owner observes the restaurant and finds the following number of customers coming for lunch each day: Monday- 30, Tuesday - 15, Wednesday- 7, Thursday 40, and Friday - 33. At a 95% confidence level determine whether the present owner reported the correct number of customers for lunch each day.
4) An employer polled its employees to see if they agree with the proposed new store hours and whether or not their present shift made a difference in their answers. The employees answered 1 for agree, 2 for don't know, and 3 for disagree. Nine first shift employees answered "agree", 15 second shift employees answered "agree", and 20 third shift employees answered agree. With a 95% confidence level determine whether or not the employees' present shift played a role in their responses to the poll.
5) A politician surveyed 100 citizens to determine if their job title had anything to do with the way they responded to the following statement: "A city-wide curfew will be put into place. Select the time that you think it should be put into place. 8pm, 9pm, or 10pm". He is mostly concerned with the 10 pm responses. 25 teachers chose 10pm, 40 doctors chose 10pm, and 35 police responded 10pm. With a 95% confidence level, determine whether job title plays a role in how the citizens responded to the statement.