Question

Part 2) FIREFLIES (7 points) Your hard work building the fancy fire pit you saw on Pinterest has really paid off! Now every weekend evening in the summer your neighbors and their kids come over to enjoy conversation, games, and cool beverages with you and your family. One parent has managed to convince the kids to put down their tablets and phones and play by catching fireflies. You make a game out of it by seeing how many they can catch every 15 minutes. You collect the data of random samples below, which shows how many fireflies the kids catch every 15 minutes. Assuming this data comes from a normally distributed population – can you conclude that the average number of fireflies caught after 9pm was different from the average caught before 9pm? Use α = 0.10. Using a TI-84.

Before 9pm

After 9 pm

6	8	12	9	15	12	9	14
8	13	11	10	10	12	8	10

1. What is the name of the type of hypothesis test required here? Is this a left-tailed, right-tailed, or two-tailed test? State AND verify all assumptions required for this test.

2. State the null and alternate hypotheses for this test: (use correct symbols and format!)

Null hypothesis

Alternate hypothesis

3. Run the correct hypothesis test and provide the information below. Give the correct symbol AND numeric value of each of the following (round answers to 3 decimal places). Test Statistic

Critical value(s)

Degrees of Freedom

p-value

4. State your statistical decision (and justify it!)

5. Interpret your decision within the context of the problem: what is your conclusion?

6. Calculate the 90% confidence interval for the difference of the average number of fireflies caught in a 15-minute interval before 9pm and the average number of fireflies caught in a 15-minutes interval after 9pm. Show your work!

7. Does your confidence interval support or contradict your conclusion from the hypothesis test you completed? Explain how you know.

Answer 1

The problem is the example of matched pair's t- test.

part 2) 1. claim. The average number of fireflies Caught atter qpm was different from the average Caught before 9 pm Md 40 ) Md=(After a pm) (Before 9 pm) - The Matched parit to test is required hypothesis test here. . This is a twentailed test : Assumptions " is Sample observations are selected at randomai a recorded arse paired values for each observati and units. The population of (11) differences fallows Normal distribution. (10) The sample size is large enough to make a decision, All assumptions are satisfied. values is the 2. Ho: Mozo versus Hai Md to. Nul hype thesis Hoi Md 20. Alternative h pothesis Hai Ma to. 2=0.10 Significance level. Sample size (m) 28 . d = std: 3 31.625 Sa-V, 6802 (8022) - (145 – (134) = 4.20 67 – .307 atstalà-M) T14250) 1.092) 1) The test statiskie talde n het liis . Con ors Degrees of Freedom an-1=8-129 At *= 0.10 lonel dfar the critical values=1-1-895, 1.895| privalue = 10.311,

4. Decision: Fail to reject the wall hypothesis (ted Here t < tesiti cal value ie te 10895. also pavalue > 0.10. 5. Interpretation. There is significant evidence to regen the claim that, the average number of fire flies Caught at ter q pm was different from the average Caught before apm. 6. The 90% contidence interval for the difference of average number of tire flies Caught CMa)= a F tari Sd) The 906. (I. = 1.625 F (1.895* 4. 207 ) = 51.194,4.444) 1. The contidence interverval support the hypothesix the Confidence interval includes test. Because decision of test is supported we zero. so the fail to reject Ho.