Problem 1 . Solve these questions and watch for the unites. a. You measure 38 wa
ID: 3181715 • Letter: P
Question
Problem 1. Solve these questions and watch for the unites.
a. You measure 38 watermelons' weights, and find they have a mean weight of 30 ounces. Assume the population standard deviation is 9.8 ounces. Based on this, construct a 99% confidence interval for the true population mean watermelon weight.
Give your answers as decimals, to two places.
.......... ± ........ ounces.
b. Two samples are taken with the following sample means, sizes, and standard deviations
¯x1 = 22 ¯x2 = 30
n1 = 60 n2 = 70
s1 = 3 s2 = 2
Find a 87% confidence interval, round answers to the nearest hundredth.
......... < 12 < ......
c. Two samples are taken with the following numbers of successes and sample sizes
r1= 27 r2 = 26
n1 = 85 n2 = 76
Find a 86% confidence interval, round answers to the nearest thousandth.
........ < p1p2 < ........
Explanation / Answer
a) mean = 30 , std.deviation = 9.8 , n = 38
z value at 99% confidence interval = 2.57
CI = mean + / - z * SE
= 30 + / - 2.57 * ( 9.8 / sqrt(38))
= (25.91 , 34.08) ounces
b) ¯x1 = 22 ¯x2 = 30
n1 = 60 n2 = 70
s1 = 3 s2 = 2
z value at 87% confidence interval = 1.51
CI = (x1 - x2) + / - z * ( s1 / sqrt(n1) +s2 / sqrt(n2))
= ( 22-30) + / - 1.51 * ( 3 / sqrt(60) + 2/ sqrt(70))
= (-8.946 , -7.054)
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