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During early evening mountain goats come down to water in a Montana loca5on. Consider each goats arrival independent of the next with arrivals consi

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Question 5

During early evening mountain goats come down to water in a Montana loca5on. Consider each goats arrival independent of the next with arrivals consistent with the rate of 4 per hour. Assume a Poisson model applies.

[a] If there is a 3-hour block of time considered early evening what is the probability that more than 10 goats will come down to water in those 3 hours?

[b] Your instructor has just seen one goat but only has of an hour more before he must go. What is the probability that he fails to see another goat before leaving?

[c] A new camera system purports to es5mate an animals height and weight from the image processed through its system. The concern is that excessive drought is limi5ng the supply of grasses and lichens at higher al5tudes and that weights may be reduced from that expected for a given height. Height es5mates are considered very good, so expected weight (from previous literature, based on height) will also be considered good. Camera-processed weight reliability is at question. Assume that weight difference from expected is distributed normally. Fifteen goats measured found that camera determined weight less expected weight had a mean and sample standard devia5on of x = 7.9lb, s=2.8lb. Test the null hypothesis H0: =0 vs Ha= <0 using the appropriate test. Use = 0.05.

[d] Someone challenged the Poisson model for goat arrival to water. Over 90 evenings during the 3-hr early evening block, the recorded number of evenings in which 0 to 10 goats were observed was 8; 11 to 15 goats were observed 45 times; 16 to 20 goats were observed 23 times; and greater than 20 goats were observed 14 times. Assume the rate is 4/hr, as noted above, and observe goats in the 4 intervals.

Find the probability for 0-10, 11-15, 16-20, and 20- under the null hypothesis. (e) Then use the Chi-Square goodness of fit test to test the Poisson model assumption. Use alpha = 0.05. Follow the guidelines for the Chi-Square test that the expected cell count should exceed 5 and combine cells as necessary.

[f] List the p-value for this test.

  • Uploaded By : Pooja Dhaka
  • Posted on : November 23rd, 2024
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