Question

How are the population mean and the mean of the sampling distribution of the mean related?

-What is the standard error of the mean? What does it measure?

-What effect does increasing sample size have on the size of the standard error?

-What does the central limit theorem state?

-What are the units of a z-score?

-How are z-scores related to standard deviation and the mean?How are they interpreted?

-Is the α always a certain value, or is it up to the investigator?

-Is the p-value of a calculated statistic a designated number, or is it up to the investigator?

-How can we reduce Type I error?

-In hypothesis testing, how can you reach a decision about the null hypothesis by comparing yourcalculated statistic to the appropriate critical value?

-In hypothesis testing, how can you reach a decision about the null hypothesis by comparing the p-value from your calculated statistic to your alpha level?

-What is the interpretation of a confidence interval?

-What determines the width of a confidence interval? How is it affected by sample size and α?

-What do we use hypothesis testing to determine? What do we use confidence intervals to determine?

-When can we use z-tests and when do we have to, instead, use t-tests?

-How does the t-distribution compare to the z-distribution?

-What does it mean when two samples are “related”?

-Given two related samples, what are “repeated measures”? What are “matched pairs”?

Answer 1

How are the population mean and the mean of the sampling distribution of the mean related?

Population mean and mean of the sampling distribution of the mean are always equal.

-What is the standard error of the mean? What does it measure?

Standard error of the mean is the ratio of the standard deviation and square root of the sample size n. It measure the standard variation in the mean.

-What effect does increasing sample size have on the size of the standard error?

If we increase sample size, the standard error decreases.

-What does the central limit theorem state?

Central limit theorem state that as we increase the sample size n, the sampling distribution of any sample statistic approaches to the approximate normal distribution.

-What are the units of a z-score?

Z-score is unit less quantity.

-How are z-scores related to standard deviation and the mean?How are they interpreted?

Z scores gives the distance from the mean in terms of multiples of standard deviation. They are interpreted as standard normal scores for respective scores.

-Is the α always a certain value, or is it up to the investigator?

NO, alpha is not always a certain value, it is up to the investigator.

-Is the p-value of a calculated statistic a designated number, or is it up to the investigator?

The p-value is the calculated statistic a designated number and it is not up to the investigator.

-How can we reduce Type I error?

By increasing significance level and sample size, we can reduce type I error.

-In hypothesis testing, how can you reach a decision about the null hypothesis by comparing yourcalculated statistic to the appropriate critical value?

For taking decision about null hypothesis we compare the test statistic value with critical value or p-value with the alpha value.

-In hypothesis testing, how can you reach a decision about the null hypothesis by comparing the p-value from your calculated statistic to your alpha level?

If the p-value is less than alpha value, then we reject the null hypothesis, otherwise we do not reject the null hypothesis.

-What is the interpretation of a confidence interval?

We are specific percent confident that the population parameter will lies between the given two bounds.

-What determines the width of a confidence interval? How is it affected by sample size and α?

The margin of error determines the width of a confidence interval. If sample size increases, width increases. If alpha increases, the width of confidence interval also increases.

-What do we use hypothesis testing to determine? What do we use confidence intervals to determine?

WE use hypothesis testing to determine whether the null hypothesis is to be reject or not. We use the confidence interval to determine the upper and lower bounds for the population parameter.

-When can we use z-tests and when do we have to, instead, use t-tests?

We use z test when we know the population standard deviation and we use t test when we don’t know population standard deviation.

-How does the t-distribution compare to the z-distribution?

For large sample size, t-distribution is same as the z-distribution.

-What does it mean when two samples are “related”?

Samples are related means there is one to one relationship between the observations of both samples.

-Given two related samples, what are “repeated measures”? What are “matched pairs”?

Repeated measures means the samples are independent and matched pairs means the samples are dependent.