gives off a \"powerful nsh and faeces\" (Beath 1996) The flowers smell this way
ID: 3073364 • Letter: G
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gives off a "powerful nsh and faeces" (Beath 1996) The flowers smell this way because their prin- cipal pollinators are carrion beetles, who are the number of carrion beetles (Phaeochrous species. The data are as follows: 120 100 80 60 40 20 attracted to such a smell. Beath (1996) observed A. amplus) that arrive per night to flowers of this 51, 45, 61, 76, 11. 117, 7. 132, 52, 149 5 6789 10 1 a. What is the mean and standard deviation of beetles per flower? b. What is the standard error of this estimate of 2000 the mean? sote answ 1500 Give an approximate 95% confidence inter- val of the mean. Provide lower and upper c. . 1000 limits d. If you had been given 25 data points instead of 10, would you expect the mean to be greater, less than, or about the same as the 500 5 6 789 10 11 mean of this sample? e. If you had been given 25 data points instead of 10, would you have expected the standard deviation to be greater, less than, or about the same as this sample? If you had been given 25 data points instead of 10, would you have expected the standard error of the mean to be greater, less than, or about the same as this sample? 200 150 f. C. 100 50 . The following three histograms (A, B, and C) plot information about the number of hours of 5 6 789 10 11 sleep adult Europeans get per night (Roenneberg a. Identify which graph goes with which b. What features of these distributions allowed c. Estimate by eye the approximate population 2012). One of them shows the frequency distri- bution of individual values in a random sample. distribution. Another shows the distribution of sample means you to distinguish which was which? for samples of size 10 taken from the same population. Another shows the distribution of mean of the number of hours of sleep using the distribution for the data. Estimate by eye the approximate mean of th distributions of sample means. sample means for samples of size 100. d.Explanation / Answer
Since you have highlighted the question numner 9, I am answering that one.
(9)
The three distributions given to us are:
(i) and (ii):
The bottom two distributions are sampling distributions of sample means. From the Central Limit theorem, we know that for a sampling distribution of sample means, the mean of the distribution is the same as the original population, but the standard deviation (also called as standard error of mean) is calculated using the formula:
Standard error = Population standard deviation/(Sample size)0.5
This means that for smaller sample sizes, the standard error is large, so the distribution is more spread out around the mean.
When sample size increases, the standard error decreases and hence the spread of the data also decreases.
We see that B has highest spread, so it must be the original population.
Since A has larger spread than C, this means it has higher standard error. So this must mean that it has a smaller sample size.
So the correct answer is:
A -> Distribution of sample means of sample size = 10
B -> Frequency distribution for individual values
C -> Distribution of sample means of sample size = 100
(iii)
For estimating the population mean, we look at the distribution B and see where its center lies. It is almost symmetric with a mean equal to 7.9
So population mean = 7.9 hours approx
(iv)
For estimating the population mean, we look at the distributions A and C and see where their centres lie. They are almost symmetric with a mean equal to 7.8.
So approx. mean of distribution of sample means = 7.8 hours approx
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