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
BEACH VACATION
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% |
What type of hypothesis test is required here? Verify all assumptions required for this test: State the null and alternate hypotheses for this test: (use correct symbols and format!) Fill in the table of expected values below. Round each value to 2 decimal places.
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|
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 =
State your statistical decision (and justify it!). Interpret your decision within the context of the problem: what is your conclusion?
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