Hypothesis Testing<\/p>\n
Student\u2019s Name<\/p>\n
Institution Affiliation<\/p>\n
Course Name and Code<\/p>\n
Professor\u2019s Name<\/p>\n
Date<\/p>\n
Hypothesis Testing<\/p>\n
The null and alternative hypotheses <\/p>\n
The parameter of interest here is the population mean (\u00b5), which is the diameter of part produced by a test run. The null hypothesis, the mean diameter of parts produced by a test run is equal to 6 inches, is represented by H0, while the alternative hypothesis, diameter of parts produced by a test run is not equal to 6 inches, is represented by H1. Thus;<\/p>\n
H0: \u00b5 = 6 inches <\/p>\n
H1: \u00b5 \u2260 6 inches<\/p>\n
The decision rule assuming that n = 200 and \u03b1 = 0.01<\/p>\n
Because the sample size (n=200) is sufficiently larger, by Central Limit Theorem (CLT), the sample mean follows a normal distribution. Therefore, the decision rule holds that reject H0 if \u2223z\u2223>z\u03b1\/2. Since the level of significance (\u03b1) = 0.01, we use excel to find z0.005.<\/p>\n
z0.005. = 2.575829304.<\/p>\n
Thus, the decision rule is as follows:<\/p>\n
Reject H0 if z < -2.575829304 or z > 2.575829304; where z is the test statistic. <\/p>\n
What the Lazer Company should conclude if the sample mean diameter for the 200 parts is 6.03 inches.<\/p>\n
z = x\u02c9- \u00b5\u1e9fn,<\/p>\n
Where;<\/p>\n
x\u02c9 – Sample mean<\/p>\n
\u00b5- population mean<\/p>\n
\u1e9f – Standard deviation<\/p>\n
n \u2013 Sample size<\/p>\n
z = 6.03- 60.1200,<\/p>\n
From excel, z= 4.242640687<\/p>\n
Recommendation<\/p>\n
Based on the earlier developed decision rule, we reject H0 since |z = 4.242640687| > 2.575829304. At 0.01 significance level, there is sufficient evidence to conclude that the mean diameter of part for Boeing Corporation produced by the test run is not equal to 6 inches. Thus, the Lazer Company should conclude that the mean diameter of a part of Boeing Corporation from the test run differs from the contract\u2019s requirement.<\/p>\n","protected":false},"excerpt":{"rendered":"
Hypothesis Testing Student\u2019s Name Institution Affiliation Course Name and Code Professor\u2019s Name Date Hypothesis Testing The null and alternative hypotheses<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-49860","post","type-post","status-publish","format-standard","hentry"],"yoast_head":"\n