Question

 

T / F	12.	A 95% confidence interval of ________ means that there is a 95% chance that the population mean falls within the range between 5.1 and 6.1.
T / F	13.	Mean is more sensitive to extreme values than median.
T / F	14.	A sampling distribution describes the distribution of a particular sample characteristic for all possible samples, random or not, of a specific sample size.
T / F	15.	t-distribution has a higher skewness than z-distribution.
T / F	16.	When the variance of a population proportion is unknown, the sampling distribution of proportions follows a t-distribution with d.f. = n–1.
T / F	17.	Central limit theorem provides a probability theory for all kinds of statistical inferences.
T / F	18.	Sometimes the standard error of a variable is larger than the standard deviation of a variable.
T / F	19.	A large sample size helps to eliminate sampling error.
T / F	20.	For a binary variable, coded 0 or 1 for the two possible outcomes, the mean indicates the proportion of cases coded 1.
T / F	21.	For a binary variable, coded 0 or 1 for the two possible outcomes,  the mean and standard deviation are not independent of each other.
T / F	22.	There is a trade-off between confidence level and precision of an interval estimation of the population mean, given a fixed sample size.
T / F	23.	________ is a correct way of setting up the null hypothesis
T / F	24.	If a test statistic has a two-tailed p-value of 0.12, its one-tailed p-value is 0.24.
T / F	25.	z-distribution is a special case of the t-distribution.
T / F	26.	In hypothesis testing, we use sample data to calculate critical value of the t- or z-score.
T / F	27.	A two-tailed test with _______ implies that the zone of rejection on the right hand side has a probability of 0.05.
T / F	28.	When calculating the power of a test, we assume that the null hypothesis is false.
T / F	29.	Changing from a 95% confidence interval estimate for a population proportion to a 99% confidence interval estimate increases the interval length by 4%.
T / F	30.	The amount of Type I error is determined by the standard error of the sampling distribution.

Answer 1

12. True... Confidence level can be defined as the probability that the value of a certain parameter (mean for this case) falls within a specified range of values.

Here, if the 95% confidence level is 5.1 to 6.1 then it means that there is a 95% chance that the population mean falls within the range between 5.1 and 6.1.

A 95% confidence interval of the mean/average means that there is a 95% chance that the population mean falls within the range between 5.1 and 6.1.

13. True... The difference between mean and median is that the mean is much more sensitive to extreme values than that of the median. It can be stated that if one or two extreme values of the data changes, the mean will change a lot but the median don't change very much. Thus, the median is much more robust than the mean as explained in the example below:

Say 1, 2, 3, 4, 5 are the data, Here median is (n+1)/2 th term i.e. (5+1)/2 th term = 3rd term = 3

Mean = (1+2+3+4+5)/5 = 3

Now, the extreme values are changed as 2, 2, 3, 4, 6

Here median will be same as per the formula i.e. 3rd term = 3

Mean will be (2+2+3+4+6)/5 = 3.4

This means mean changed a lot but the median is not.

14. The sampling distribution of any particular statistic can be defined as the distribution of that particular statistic, considered to be a random variable, if derived from a particular random sample of size . It may also be considered as the distribution of that particular statistic for all the samples that is possible from the same population of a given sample size.

15. False, Skewness for Z and T distribution is 0. Z distribution is for a sample size more than 30 and T is for less than 30.

16. True, T distribution is followed only if the sample size is less than 30 and the population standard deviation/variance is unknown.

In this case the sample standard deviation is taken into consideration.

The formula is shown below:

17. False,

19. True, Sample Size is inversely proportional to Sampling Error. So if the sample size increases, the sampling error gets reduced.

23. The null hypothesis always states that the population parameter is equal to the value that is claimed. For example, if it was a belief that the average height of man is 5.5 feet, then the null hypothesis will be:

H₀: U = 5.5 ... (U is the Mean/Average)

H₀ is the Null Hypothesis.

24. False, If the P value for Two Tailed is 0.12, then for the single tailed, it will be 0.12/2 = 0.06.

The P Value of a Two Tailed always becomes double of its Single Tailed P value.

25. False, T distribution is a special case of Z distribution.

Z distribution is for a sample size more than 30 and T is for less than 30.

The distribution graph almost looks similar (Bell Curve)

26. True, Self Explanatory

27. A two-tailed test with 90% confidence level implies that the zone of rejection on the right hand side has a probability of 0.05.

If the confidence level is 90%, Alpha is 0.1, hence, in case of a two tailed, it gets halved i.e. 0.05 on both the tails.

28. True, The Power of a hypothesis test (Beta) is the probability of not accepting the null hypothesis when the null hypothesis is false.

29. False, Changing from a 95% confidence interval estimate for a population proportion to a 99% confidence interval estimate increases the interval length by 31%.

30. False, The Standard Deviation (Sigma) of a Sampling Distribution for a given statistic is frequently called as the Standard Error of that particular Statistic.