Question

True or false?

a) The larger sample size, the narrower confidence interval is obtained.

b) Correlation coefficient does have same units as explanatory variable.

c) The normal curve is symmetric and double-peaked.

d) An explanatory variable is always scaled on the x-axis.

e) Graph that displays association between two variables is called a stemplot.

f) If two-sided test has to be used, the alternative hypothesis must have a form of typical inequality.

g) In comparing two population means (or proportions), in the null hypothesis we always assume there is no difference between two population means (or proportions).

Answer 1

a) The larger sample size, the narrower confidence interval is obtained.

The margin of error in a confidence interval is always inversely proportional to the sample size, i.e, larger the sample smaller the margin of error. We know that, smaller the margin of error, narrower the interval. Therefore, larger the sample size, narrower is the interval. Answer : True

b) Correlation coefficient does have same units as explanatory variable.

It might happen that the explanatory variables have a diffferent sign but the relationship is in a positive direction, or , vice versa. Therefore, the statement is true.

c)The normal curve is symmetric and double-peaked.

We know that, the normal curve is bell shaped and it symmetric, but with one peak. Therefore, the statement is false. Answer : False

d) An explanatory variable is always scaled on the x-axis.

Yes, the explanatory variable is always scaled on the x axis. Answer : True

e) Graph that displays association between two variables is called a stemplot.

We know that, a stemplot shows us how individual values are distributed within a data. Itdoes not show association between two variables. Answer : False

f) If two-sided test has to be used, the alternative hypothesis must have a form of typical inequality.

In a two sided test, the alternative hypothesis has a sign , whereas a typical inequality has the signs < or >(less than or greater than). Therefore, the statement is false. Answer : False

g) In comparing two population means (or proportions), in the null hypothesis we always assume there is no difference between two population means (or proportions).

In comparing two means or proportions, we always keep the null hypothesis assuming no difference between the two. Answer : True