niology 218 13) You sample 25 black turban smails from the toceal ogodi s a the

Question

niology 218 13) You sample 25 black turban smails from the toceal ogodi s a the mean size in your sample is 32.7mm. You (somelow) know that the deviation, . for this population is 3.1 mm. of snails and findt true manvdard a) What are the endpoints of a 99% confidence interval for these data? (4 points) b) Explain in words what this confidence interval tells us.(3 points) c) what is the margin of error for an 80% confidence interval for these same data? (3 points) d) Your work on this snail has shown that individuals smaller than 20.0 mm are not sexually mature yet. What proportion of your sample would you immature? (4 points) expect to be sexually

Explanation / Answer

a) n=25 sample is provided,

mu = 32.7

sd= 3.1

So., we need to find 99% conf interval and so for that we need z values for the same

Using the below equation we will be able to find the 99% conf interval

X' = mu + z*sd/sqrt(n)

Z values will be -/+ 2.58 for 99% confidence interval. (From z table look for values of z at area of 0.005 and 0.995

So., X'= 32.7 +/- 2.58*3.1/sqrt(25)

So., X'= 31.1004 and 34.2996 (End points of 99% conf )

b) This conf interval tells us that there are 99% chances of the distribution whose mean is 32.7 and sd = 3.1 to have a randomly picked value to be between 31.1 to 34.2996

i.e. there is only 1% probability that the snail's mm will be outside the range of 31.1 to 34.2996

c) Margin of error for the same sample with 80% conf interval will be

X'= 32.7 +/- 1.28*3.1/sqrt(25)

X' range will be 31.90544 to 33.49456

So margin of error will be 20% to have the data not falling in this range

d) For less than 20mm we need to find the z value

z= (X'-mu)/(sd/sqrt(n))

= (20-32.7)/(3.1/sqrt(25)) =-20.48387

for the -20.48 z value p value will be approx 0% and so we can say that almost 100% of the observations will have more than 20mm and so 0% of the observations will be less than 20mm

Hope the above answer has helped you in understanding the problem. Please upvote the ans if it has really helped you. Good Luck!!

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