Tut 10

Tutorial 10 Hypotheses Testing 1. The following information is available H o : µ = 50 H 1 : µ ≠ 50 The sample mean is 49 and the sample size is 36.The population follows the normal distribution and the standard deviation is 5.Use the 0.05 significance level. 2. The Mac Burger restaurant chain claims that the waiting time of customer for service is normally distributed, with a mean of 3 minutes and a standard deviation of 1 minute. The quality-assurance department found in a sample of 50 customers at the Warren Road Mac Burger that the time waiting was 2.75 minutes. At the 0.05 significance level, can we conclude that the mean waiting time is less than 3 minutes? 3. Given the following Hypotheses H 0 : µ = 400 H 0 : µ ≠ 400 For a random sample of 12 observations, the sample mean was 407 and the sample standard deviation 6. Using the 0.01 significance level a) State the decision Rule b) Compute the value of the test statistic 4. Given the following hypothesis H O : µ = 100

a. b. c. d.

H O : µ ≠ 100 A random sample of six resulted in the following values 118, 105, 112, 119, 105, and 111. Using the 0.05 significance level, can we conclude the mean is different from 100? State the decision rule? Compute the value of statistic What is your decision regarding the null Hypotheses? Estimate the p-value?

5. Mary Jo Fitzpatrick is the Vice President for Nursing Services at St. Luke’s Memorial Hospital. Recently she noticed that unionized job for nurses seem to offer higher wages. She decided to investigate and gathered the following sample information. Group Union Nounion

Mean Wage $20.75 $19.80

Sample Standard Deviation $2.25 $1.90

Sample size 40 45

Would it be reasonable for her to conclude that union nurses earn more? Use the 0.02 significance level. What is the p-value.

6. Ms Lisa Monnin is the budget director for Nexus Media , Inc. She would like to compare the daily travel expenses for the sales staff and the audit staff. She collected the following sample information. Sales ($) Audit($)

131 130

135 102

146 129

165 143

136 149

142 120

139

At the 0.10 significance level, can she conclude that the mean daily expenses are greater for the sales staff than the audit staff? What is the p-value? 7. The null and alternate hypotheses are H 0 : µd = 0 H1 : µ d ≠ 0 8. The following paired observations show the number of traffic citation given for speeding by officer Dhont and Officer Meredith of the South Carolina Highway patrol for the last five months Officer Dhont Officer Meredith

May 30

June 22

July 25

DAY August 19

26

19

20

15

September 26 19

At the 0.05 significance level, is there a difference in the mean number of citation given by the two officers?