a)You measure 28 textbooks\' weights, and find they have a mean weight of 42 oun
ID: 3128070 • Letter: A
Question
a)You measure 28 textbooks' weights, and find they have a mean weight of 42 ounces. Assume the population standard deviation is 11.3 ounces. Based on this, construct a 95% confidence interval for the true population mean textbook weight. Give your answers as decimals, to two places
_______ < < ________
b)You are given the following hypotheses:
Ho : = 40
Ha : > 40
We know that the sample standard deviation is 10 and the sample size is 60. For what sample mean would the p-value be equal to 0.05? Assume that all conditions necessary for inference are satisfied. ______________
You are given the following hypotheses:
Ho : = 40
Ha : 40
We know that the sample standard deviation is 10 and the sample size is 60. For what sample mean would the p-value be equal to 0.05? Assume that all conditions necessary for inference are satisfied.
Lower value: __________
Upper value: __________
Explanation / Answer
A)
Note that
Margin of Error E = t(alpha/2) * s / sqrt(n)
Lower Bound = X - t(alpha/2) * s / sqrt(n)
Upper Bound = X + t(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.025
X = sample mean = 42
t(alpha/2) = critical t for the confidence interval = 2.051830516
s = sample standard deviation = 11.3
n = sample size = 28
df = n - 1 = 27
Thus,
Margin of Error E = 4.381682575
Lower bound = 37.61831742
Upper bound = 46.38168258
Thus, the confidence interval is
( 37.61831742 , 46.38168258 ) [ANSWER]
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