Determine if the following statements are true or false: 1) Decreasing the signi

Question

Determine if the following statements are true or false:

1) Decreasing the significance level will increase the probability of making a Type 1 error (i.e., rejecting H0 when it is actually true).

2) If a given value (for example, the null hypothesis value of a parameter) is within a 95% confidence interval, it will also be within a 99% confidence interval.

3) The standard error of the sample mean, x ¯   , would be larger for a sample size (n) of 25 than it would be for a sample size of 125.

1) Decreasing the significance level will increase the probability of making a Type 1 error (i.e., rejecting H0 when it is actually true).

2) If a given value (for example, the null hypothesis value of a parameter) is within a 95% confidence interval, it will also be within a 99% confidence interval.

3) The standard error of the sample mean, x ¯   , would be larger for a sample size (n) of 25 than it would be for a sample size of 125.

Explanation / Answer

1) This is false because significance level and probability of type I error are the same thing.

i.e.

significance level = Type I error

2) This is true because 99% confidence interval contains wider range and includes all the values which are there in 95% confidence interval.

3) This is true because to find the standard error, we divide the standard deviation by square root of sample size so for n = 25, the standard error will be larger as compared to for n = 125.

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