Week 9 Application Assignment
HYPOTHESIS TESTS WITH CATEGORICAL DATA
1) BEACH VACATION (5 pts)
You take your family on a wonderful, relaxing vacation to the beach. About 15 minutes after you’ve settled into the perfect spot in the sand, your oldest child tells you he’s bored. To keep him busy you tell him to collect some shells, because you read online that the beach where you’re staying is known for having lots of different colors of shells wash up on the beach. A few days later he’s collected over 500 shells, and he tallies up how many of each color he has in the table below. You’re curious if his collection of shells has the same distribution of colors as the overall beach has, so you go online and find the distribution of shell color percentages you should expect to find at that particular beach, and add those to your data table. Perform a hypothesis test to determine if the color distribution of your son’s seashell collection is what you’d expect at that beach. Use = 0.10.
| White | Red | Black | Orange | Blue | Other | Total | |
| # of Shells | 309 | 46 | 73 | 45 | 31 | 8 | |
| Expected percentages | 57% | 12% | 14% | 8% | 6% | 3% | 100% |
Step 1) What type of hypothesis test is required here?
Step 2) Verify all assumptions required for this test:
Step 3) State the null and alternate hypotheses for this test: (use correct symbols and format!)
Null hypothesis
Alternate hypothesis
Step 4) Fill in the table of expected values below. Round each value to 2 decimal places.
| White | Red | Black | Orange | Blue | Other | Total | |
| Expected # of Shells |
Run the correct test using a software and provide the information below. Use correct symbols and round answers to 3 decimal places.
Test Statistic = Degrees of freedom =
Critical Value = p-value =
Step 5) State your statistical decision (and justify it!)
Step 6) Interpret your decision within the context of the problem: what is your conclusion?
2) GIRL SCOUT COOKIES (5 pts)
You are contacted by the top cookie-selling Girl Scout troop in the city. As part of their sales plan for next year’s cookie selling season, they need to know (with 90% confidence) if the types of cookies purchased by their customers depends on where the scouts sell them. Here is their confidential sales data from last year:
| Type of Cookie Sold | ||||||
| Thin Mints | Tagalongs | Do-si-dos | Trefoils | Samoas | ||
| Sales Method | At parents’ workplace | 472 | 641 | 350 | 223 | 401 |
| Door-to-Door | 840 | 1092 | 673 | 511 | 542 | |
| Community Events | 683 | 742 | 491 | 420 | 374 | |
Step 1) What type of hypothesis test is required here?
Step 2) Verify all assumptions required for this test:
Step 3) State the null and alternate hypotheses for this test:
Null hypothesis
Alternate hypothesis
Step 4) Run the correct test using a software and provide the information below. Use correct symbols and round answers to 3 decimal places.
Test Statistic = Degrees of freedom =
Critical Value = p-value =
Fill-in the Expected Values of each cell below. Round answers to 2 decimal places.
(Hint: use the output of the statistical test you ran above!)
| Type of Cookie Sold | ||||||
| Thin Mints | Tagalongs | Do-si-dos | Trefoils | Samoas | ||
| Sales Method | At parents’ workplace | |||||
| Door-to-Door | ||||||
| Community Events | ||||||
Step 5) State your statistical decision (and justify it!)
Step 6) Interpret your decision within the context of the problem: what is your conclusion?
3) MANUFACTURING PRODUCTIVITY (6 pts)
You are an Operations Manager for a local steel manufacturing company, and you are in the process of selecting a vendor for a new type of metal finishing machine. For the past week you’ve tested machines from three different companies and collected the randomly sampled data below that shows how many parts each machine produced in seven different one-hour periods over the course of your manufacturing test. Is the average production of these machines the same, or is one of them different from the others? [If the productivity is the same, you will simply choose the machine with the lowest cost.] You may assume that all populations are independent and nearly normal. Test at the 95% confidence level. (i.e. α= 0.05)
Parts produced per hour for machines from three vendors:
| Machine A | Machine B | Machine C |
| 112 | 116 | 102 |
| 104 | 118 | 107 |
| 116 | 112 | 108 |
| 98 | 108 | 92 |
| 109 | 113 | 114 |
| 111 | 117 | 105 |
| 115 | 107 | 102 |
Step 1) What type of hypothesis test is required here?
Step 2) Verify all assumptions required for this test:
Step 3) State the null and alternate hypotheses for this test: (use correct symbols and format!)
Null hypothesis
Alternate hypothesis
Step 4) Run the correct using a software and provide the information below. Use correct symbols and round answers to 3 decimal places.
Test Statistic = Degrees of freedom (1st) =
Critical Value = Degrees of freedom (2nd) =
p-value =
Step 5) State your statistical decision (and justify it!)
Step 6) Interpret your decision within the context of the problem: what is your conclusion?
