Two friends. Karen and Jodi, work different shifts for the same ambulance service. They wonder if the different shifts average different numbers of calls. Looking at past records, Karen determines from a random sample of 39 shifts that she had a mean of 4.7 calls per shift. She knows that the population standard deviation for her shift is 1.5 calls. Jodi calculates from a random sample of 31 shifts that her mean was 5.4 calls per shift. She knows that the population standard deviation for her shift is 1.2 calls. Test the claim that there is a difference between the mean numbers of calls for the two shifts at the 0.02 level of significance. Let Karen's shifts be Population 1 and let Jodi's shifts be Population 2 . Step 1 of \( 3: \) state the null and alternative hypotheses for the test. Fill in the blank below. \[ H_{0}: \mu_{1}=\mu_{2} \] \( H_{a}: \mu_{1} \)

1. Suppose you own a hat shop and decide to order hats in only one size for the coming season. To decide which size to order, you look at last year's sales figures, which are itemized according to size. Should you find the mean, median, or mode for the data? Why? 2. A movie chain conducts a popcorn poll in which each person entering a theater and buying a box of popcorn is asked a yes-no question. Which "average" do you think is used to report the result and why? 3. When a government agency reports the average rainfall for a state for a year, which "average" do you think it uses and why? 4. Karl had scores of \( 90,95,85 \), and 90 on his first four tests. a. Find the median, mean, and mode. b. Karl scored a 20 on his fifth exam. Which of the three averages would Karl want the instructor to use to compute his grade? Why? c. Which measure is affected most by an extreme score?

9. The owners of a restaurant want to address their concerns of declining customer satisfaction. Examine the following sampling methods for bias. Which would provide good feedback? Why? i. A postcard questionnaire is placed with every bill in hopes that patrons fill it out at home and mail it back. ii. Servers are instructed to encourage patrons to visit the web site, the address of which is printed on the bottom of the receipt, hosting a short survey. iii. Patrons can fill out a questionnaire at the bar and drop it in a locked box, thereby entering a drawing for a free dinner for two. iv. A pollster is hired to stand outside the restaurant and ask every other exiting patron some questions.

HEB finds 241 out of 503 people prefer Pepsi products wihle Kroger finds 301 out of 550 prefer Pepsi. At the .07 level, test if HEB is lower, Critical Calue Blank 1 Test Statistic Blank 2 p.Value Blank 3

Gary has discovered a new painting tool to help him in his work. If he can prove to himself that the painting tool reduces the amount of time it takes to paint a room, he has decided to invest in a tool for each of his helpers as well. From records of recent painting jobs that he completed before he got the new tool, Gary collected data for a random sample of 6 medium-sized rooms. He determined that the mean amount of time that it took him to paint each room was 4.6 hours with a standard deviation of 0.3 hours. For a random sample of 9 medium-sized rooms that he painted using the new tool, he found that it took him a mean of 4.1 hours to paint each room with a standard deviation of 0.4 hours. At the 0.10 level, can Gary conclude that his mean time for painting a medium-sized room without using the tool was greater than his mean time when using the tool? Assume that both populations are approximately normal and that the population variances are equal. Let painting times without using the tool be Population 1 and let painting times when using the tool be Population 2. Step 3 of 3 : Draw a conclusion and interpret the decision.

Company X is known to release some employees and hire new ones every year without changing the total number of employees in the company. A statistical analysis was done, and the following was observed: in year 2020, there were 150 male employees who constituted \( 75 \% \) of the total number of employees. In year \( 2021,60 \% \) of the employees were females. What is the change in the number of female employees from year 2020 to 2021 ?