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Given the hypothesis testing solution ,give an example for each of the Type I and Type II errors.

Given the hypothesis testing solution ,give an example for each of the Type I and Type II errors.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 40CR
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Given the hypothesis testing solution ,give an example for each of the Type I and Type II errors.

 

By using t statistic as hypothesis test, o of the population data is not known and oʻx=o°y Variable X Variable Y n=50, x=1197.32, s,=11510.67 m=50, y=1297.18, s, = 10689.86 Let ug = mean brain weights of female of age <18, µ, = mean brain weights of male age <18 Ho: Hx = Hy H1: Hx < Hy (LTT) 49(11510. 67) + 49(10689. 86) 50 + 50 – 2 Pooled Variance, sp = 11100.27 (1197. 32 – 1297. 18)–0 t= -4.7391 V11100. 27( + ) p-value approach, a= 0.05 P(T<-4.7391) = 3.63594x10-6= 0.00000363594 p-value < 0.05, Hence reject null hypothesis Ho. At a= 0.05, We have sufficient evidence to conclude that mean of brain weights of brain weights of female of age <18 is lesser than mean brain weights of male of age <18
Transcribed Image Text:By using t statistic as hypothesis test, o of the population data is not known and oʻx=o°y Variable X Variable Y n=50, x=1197.32, s,=11510.67 m=50, y=1297.18, s, = 10689.86 Let ug = mean brain weights of female of age <18, µ, = mean brain weights of male age <18 Ho: Hx = Hy H1: Hx < Hy (LTT) 49(11510. 67) + 49(10689. 86) 50 + 50 – 2 Pooled Variance, sp = 11100.27 (1197. 32 – 1297. 18)–0 t= -4.7391 V11100. 27( + ) p-value approach, a= 0.05 P(T<-4.7391) = 3.63594x10-6= 0.00000363594 p-value < 0.05, Hence reject null hypothesis Ho. At a= 0.05, We have sufficient evidence to conclude that mean of brain weights of brain weights of female of age <18 is lesser than mean brain weights of male of age <18
Condition checking 1: n=50 (n 230) m=50 (n 230) The sample size, n for the brain weights of female and male of age less than 18 years old (variable X and variable Y) is equals to 50. Sample size greater than or equals to 30 is usually considered as a large sample. According to the Central Limit Theorem, the sampling distribution of X and Y for a relatively large sample size is approximately normal, irrespective of the shape of the population distribution. To choose a distribution, first standard deviation, o of data is checked whether is known or not known, then whether oʻy= o, or of;+ o, is checked. Assume that variance for Variable X and variance of Variable Y are equal Họ: ox= o°y Based on the value obtained in descriptive statistic: ox=11510.67, o, = 10689.86 11510. 67 F= 10689. 86 = 1.0768 d= 49 df-49 0.05 Fo.025,49,49 = 1.6073 Since F < 1.6073, we cannot reject null hypothesis Ho Hence, with a= 0.05, we have sufficient statistical evidence to conclude that of=o. Since the standard deviation, o of the population data is not known and o,=o°y, t test statistic is used.
Transcribed Image Text:Condition checking 1: n=50 (n 230) m=50 (n 230) The sample size, n for the brain weights of female and male of age less than 18 years old (variable X and variable Y) is equals to 50. Sample size greater than or equals to 30 is usually considered as a large sample. According to the Central Limit Theorem, the sampling distribution of X and Y for a relatively large sample size is approximately normal, irrespective of the shape of the population distribution. To choose a distribution, first standard deviation, o of data is checked whether is known or not known, then whether oʻy= o, or of;+ o, is checked. Assume that variance for Variable X and variance of Variable Y are equal Họ: ox= o°y Based on the value obtained in descriptive statistic: ox=11510.67, o, = 10689.86 11510. 67 F= 10689. 86 = 1.0768 d= 49 df-49 0.05 Fo.025,49,49 = 1.6073 Since F < 1.6073, we cannot reject null hypothesis Ho Hence, with a= 0.05, we have sufficient statistical evidence to conclude that of=o. Since the standard deviation, o of the population data is not known and o,=o°y, t test statistic is used.
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