PLEASE ANSWER THIS FOR ALL OF THE THREE FOLLOWING QUESTIONS! For each situation

Question

PLEASE ANSWER THIS FOR ALL OF THE THREE FOLLOWING QUESTIONS! For each situation below answer these three questions: Do not do a full hypothesis test. Only answer the questions. a. State the relevant hypothesis test: • Two-sample Matched Pairs t-test for means • Two-sample Independent t-test for means • Two-sample proportion z-test for proportions b. Define parameters and state the null and alternative hypothesis c. Based on the hypotheses, state what it would mean to commit a Type I error and a Type II error in context of the situation

a) An automobile company wants to compare two styles of front bumpers. They randomly sample 20 different types of car and select two of each type of car for their test. The company fits the first bumper style to one car and the second bumper style to the second car of the same type. They then crash all the cars into a concrete wall and measure the repair costs. The company wants to know if the repair costs of the cars using the first bumper is less than the repair costs of the cars using the second bumper.

Explanation / Answer

a) paired t-test , for matched paired we used the paired t-test,
hypothesis for paired t-test would be,

H0- d=0 , i.e there is no any post effect

H1- there is post effect

second - two sample t-tes?t

H0- there is significant effect between two means
H1- there is not sifnifican effect between two means

3- two sample z-test for praportion

b) pared t-test

parameter- Mpre , and Mpost.
H0: Mpost-Mpre=0 H1: not equal to zero

Two sample t-test

M1 -first group mean, M2 - group 2 mean

H1:M1=M2 and H1:   M1 not =/   M2

c) type one error is the reject H0 when the H0 is true and type 2 error is Accet H0 when it is false . for commiting the Type one error then the propabily of reject the null hypothesis will be decress and when type two error inccress then the power of the test would be decress,

d) for camparison we use the two sample t-test becouse cars are fitted the diffreant bumpars, so there are two groups , one for 1st bumbars and second for second bumpars

so H0= both bumbars have same repaire cost

H1= bumpars have diffreant repaire cost

Thanks ?

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