3) A factory manufactures laptops. The weight of laptop follows normal distribution N (µ, σ²) independently. For quality control, an inspector sampled 4 laptops randomly and measured their weights. The measured weights are as follows in kilograms: 3.280, 1.503, 3.322, 1.502 You may assume that the smoothness condition holds. (a) Find an exact 90% confidence interval of µ. (b) Find an exact 90% confidence interval of σ². (c) The factory aims to control the average weight of the manufactured laptop to be 1kg. Based on the weights of 4 sampled laptops, test whether the factory has successfully controlled the average weight at significance level of 5%. State the null hypothesis, the alternative hypothesis, the rejection region, and the test result. (d) Find the efficiency of the sample variance S2 assume µ is known. = n³¹¹²²±1 (Xi - X)². You may n- i=1
3) A factory manufactures laptops. The weight of laptop follows normal distribution N (µ, σ²) independently. For quality control, an inspector sampled 4 laptops randomly and measured their weights. The measured weights are as follows in kilograms: 3.280, 1.503, 3.322, 1.502 You may assume that the smoothness condition holds. (a) Find an exact 90% confidence interval of µ. (b) Find an exact 90% confidence interval of σ². (c) The factory aims to control the average weight of the manufactured laptop to be 1kg. Based on the weights of 4 sampled laptops, test whether the factory has successfully controlled the average weight at significance level of 5%. State the null hypothesis, the alternative hypothesis, the rejection region, and the test result. (d) Find the efficiency of the sample variance S2 assume µ is known. = n³¹¹²²±1 (Xi - X)². You may n- i=1
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 4GP
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Transcribed Image Text:3) A factory manufactures laptops. The weight of laptop follows normal distribution N (µ, σ²)
independently. For quality control, an inspector sampled 4 laptops randomly and measured
their weights. The measured weights are as follows in kilograms:
3.280, 1.503, 3.322, 1.502
You may assume that the smoothness condition holds.
(a) Find an exact 90% confidence interval of µ.
(b) Find an exact 90% confidence interval of σ².
(c) The factory aims to control the average weight of the manufactured laptop to be 1kg.
Based on the weights of 4 sampled laptops, test whether the factory has successfully
controlled the average weight at significance level of 5%. State the null hypothesis,
the alternative hypothesis, the rejection region, and the test result.
(d) Find the efficiency of the sample variance S2
assume µ is known.
=
n³¹¹²²±1 (Xi - X)². You may
n-
i=1
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