History of Modern Ottomans
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MBA 551 Probability and Statistics
HW4
Prepared By
Gürcan BAYRAK
21303377
Q37:
Part a) In the question body, it is given that the process is designed to produce tees with a mean weight of 0,250 ounce. It is expected that the production process has a mean of 0,250 ounce. So, the hypothesis can be constructed as following:
H0 = Production Process equals to 0.250 ounce.
Ha = Production Process does not equal to 0.250 ounce.
Part b) If the sample data is analyzed the sample mean and the sample standard deviation equal the following values:
x̄:0,25248
s:0,00223
Part c) In order to calculate the test statistics, it is suitable to decide on statistical distribution. In the question body, the variance of the population is not given. So, using t distribution will be meaningful.
t n-1 = (x̄ - µ0) / (s/n1/2) where n= 40
t 39 = 7,03
Part d) The p value of the test statistics is a very small number close to 0. (In Minitab 0,000 is obtained as p value)
Part e) By using α=.01 the following rejection region is obtained. It is seen that the t value is in the rejection region. Also the p value is extremely small and less than α, rejecting H0 is statistically acceptable decision.
7,03
Reject H0
Reject H0
/2=.025
-t n-1,α/2
Do not reject H0
/2=.025
-2.021
2.021
t n-1,α/2
Part f) The data given in the question body, provides sufficient data to conclude that the process is not operating satisfactorily. P value which is given in part d and rejection region representation which is given in part e give the basis for the rejection.
Part g) In the context of the problem, it makes sense to call α as producer risk because α represents the type I error which means rejecting a true H0. In H0 it is claimed that the true mean equals to 0,250 ounce and α represents the rejecting probability of having acceptable mean of production. On the other hand, it makes sense to call β as the consumer risk because β represents the type II error which means failing to...
HW4
Prepared By
Gürcan BAYRAK
21303377
Q37:
Part a) In the question body, it is given that the process is designed to produce tees with a mean weight of 0,250 ounce. It is expected that the production process has a mean of 0,250 ounce. So, the hypothesis can be constructed as following:
H0 = Production Process equals to 0.250 ounce.
Ha = Production Process does not equal to 0.250 ounce.
Part b) If the sample data is analyzed the sample mean and the sample standard deviation equal the following values:
x̄:0,25248
s:0,00223
Part c) In order to calculate the test statistics, it is suitable to decide on statistical distribution. In the question body, the variance of the population is not given. So, using t distribution will be meaningful.
t n-1 = (x̄ - µ0) / (s/n1/2) where n= 40
t 39 = 7,03
Part d) The p value of the test statistics is a very small number close to 0. (In Minitab 0,000 is obtained as p value)
Part e) By using α=.01 the following rejection region is obtained. It is seen that the t value is in the rejection region. Also the p value is extremely small and less than α, rejecting H0 is statistically acceptable decision.
7,03
Reject H0
Reject H0
/2=.025
-t n-1,α/2
Do not reject H0
/2=.025
-2.021
2.021
t n-1,α/2
Part f) The data given in the question body, provides sufficient data to conclude that the process is not operating satisfactorily. P value which is given in part d and rejection region representation which is given in part e give the basis for the rejection.
Part g) In the context of the problem, it makes sense to call α as producer risk because α represents the type I error which means rejecting a true H0. In H0 it is claimed that the true mean equals to 0,250 ounce and α represents the rejecting probability of having acceptable mean of production. On the other hand, it makes sense to call β as the consumer risk because β represents the type II error which means failing to...