State whether the following statements are True or False. A type I error is the

Question

State whether the following statements are True or False.

A type I error is the mistake of rejecting the null hypothesis when it is actually false. T

Two samples are independent if the sample values selected from one population are not related to the sample values from the other population

The null hypothesis (denoted by H0) isa statement that the value of a population parameter is equal to some value.

In case of hypothesis testing for a sample, the t statistic is used if is not known and sample size n is greater than 5

A claim that two population proportions are equal, each of the two samples must satisfy the requirement that and .          

In an unpaired samples t-test with sample sizes n1= 21 and n2= 11, the value of t should be obtained at 32 degree of freedom.

Explanation / Answer

Solution:-

1) FALSE - A type I error is the mistake of rejecting the null hypothesis when it is actually false.

(A type I error is the mistake of rejecting the null hypothesis when it is actually TRUE.)

2) TRUE - Two samples are independent if the sample values selected from one population are not related to the sample values from the other population.

(Definitions Two samples are independent if the sample values selected from one population are not related to or somehow paired or matched with the sample values selected from the other population. If there is some relationship so that each value in one sample is paired with a corresponding value in the other sample, the samples are dependent. )

3) TRUE - The null hypothesis (denoted by H0) is a statement that the value of a population parameter is equal to some value.

(The null hypothesis will be a statement on the value of a population parameter, usually the mean value if a question relates to return, or the standard deviation if it relates to risk. It can also refer to the value of any random variable. In hypothesis testing, the null hypothesis is initially regarded to be true, until (based on our process) we gather enough proof to either reject the null hypothesis, or fail to reject the null hypothesis.)

4) FALSE - In case of hypothesis testing for a sample, the t statistic is used if is not known and sample size n is greater than 5.

(In case of hypothesis testing for a sample, the t statistic is used if is not known and sample size n is greater than 30.)

5) TRUE - A claim that two population proportions are equal, each of the two samples must satisfy the requirement that np 5 and nq 5

and .          

6) FALSE - In an unpaired samples t-test with sample sizes n1= 21 and n2= 11, the value of t should be obtained at 32 degree of freedom.

(df = n1 + n2 - 2 ---> 21+11-2 = 30 should be the degree of freedom for n1 = 21, and n2 = 11)

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