MATH SOLVE

2 months ago

Q:
# Question Part Points Submissions Used Problem 10-9 A sample of 80 observations is taken from a population of unknown mean wherein the standard deviation is assumed to be 5 grams. The computed value of the sample mean is 32.7 grams. Construct confidence intervals for each of the following levels of confidence:90% confidence interval : ______

Accepted Solution

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Answer:The 90% confidence interval is (31.78 grams, 33.62 grams).Step-by-step explanation:The first step is finding our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], that is between [tex]Z = 1.64[/tex] and [tex]Z = 1.65[/tex], so we use [tex]z = 1.645[/tex].Now, find M as such:[tex]M = z*\frac{\sigma}{\sqrt{n}} = 1.645*\frac{5}{\sqrt{80}} = 0.92[/tex]In which [tex]\sigma[/tex] is the standard deviation and n is the length of the sampleThe lower end of the interval is the sample mean subtracted by M. So it is 32.7 - 0.92 = 31.78 grams.The upper end of the interval is the sample mean added to M. So it is 32.7 + 0.92 = 33.62 grams.The 90% confidence interval is (31.78 grams, 33.62 grams).