1. Gentle Ben is a Morgan horse at a Colorado dude ranch
Question and Solution
1. Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following gluco
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1. Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100ml).
93, 88, 82, 105, 99, 110, 84, 89
The sample mean is xbar = 93.8. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know from past experience that = 12.5. The mean glucose level for horses should be = 85mg/100ml. Do these data indicate that Gentle Ben has an overall average glucose level higher that 85? Use a = 0.05.
2. For healthy adults, the red blood cell volume mean is about = 28ml/kg. Suppose Roger has had 7 blood tests, and the red blood cell volumes were:
32, 25, 41, 35, 30, 37, 29
The sample mean is xbar = 32.7ml/kg. Let x be a random variable that represents Rogerâ€™s red blood cell volume. Assume that x has a normal distribution and = 4.75. Do the data indicate that Rogerâ€™s red blood cell volume is different (either way) from = 28ml/kg? Use a 0.0a level of significance.
3. Let x be a random variable that represents the pH of arterial plasma. The mean of the x distribution is = 7.4. A ransom sample of 31 patients with arthritis took a drug from 3 months. Tests showed the average pH to be xbar = 8.1 with sample standard deviation s = 1.9. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood.
4. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is = 19 inches. However a report has said that for a random sample of 51 fish caught, the mean length was xbar = 18.5 inches with estimated standard deviation s = 3.2 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than = 19 inches? Use a = 0.05.
5. The mean shopping time for a woman accompanied by children in national houseware stores is 7.3 minutes. A random sample of women shoppers with children at Cherry Creek gave the following shopping times in minutes:
Confirm with calculator that mean is xbar = 8.1, and standard deviation s = 1.4 min. Assume shopping time follows an approximately normal distribution. Use 5% level of significance to test that the average shopping time for women with children at Cherry Creek is higher than the national average for this type of store.
6. Women at U of C have a long term graduation rate of 67%. Over the past several years a random sample of 38 women at the school showed that 21 eventually graduated. Does this indicate that the population proportion of women who graduate from U of C is now less than 67%? Use a 5% level of significance.
7. A lodge advertises that 75% of its guests catch northern pike over 20 pounds. Suppose that last summer 64 out of a random sample of 83 guests did, in fact, catch northern pike weighing over 20 pounds. Does this indicate that the population proportion of guests who catch pike over 20 pounds is different from 75% (either higher or lower)? Use a = 0.05.
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