a researcher selects a sample from a population with μ = 30 and uses the sample to evaluate the effect of a treatment. after treatment, the sample has a mean of m = 32 and a variance of s2 = 6. which of the following would definitely increase the likelihood of rejecting the null hypothesis?

question options:

a.
decrease the sample variance
b.
increase the sample mean
c.
increase the sample size
d.
all of the other options will increase the likelihood of rejecting the null hypothesis

Option b) Increase the sample mean

Step-by-step explanation:

Given that a researcher selects a sample from a population with μ = 30 and uses the sample to evaluate the effect of a treatment. After treatment, the sample has a mean of M = 32 and a variance of s2 = 6.

This is a paired test with test statistic

=mean diff/std error

Mean difference would increase if sample mean increases.

This would increase the test statistic

Or otherwise decrease in variance will increase the test statistic

Or Increase in sample size would also increase test statistic

Of all these the II option is definite in increasing the  likelihood of rejecting the null hypothesis because this would definitely increase the chances of rejecting H0.

Others may also have effect but not as much direct as sample mean difference.

Because variance and sample size have influence only upto square root of the difference.

the correct answer is you spend $55.78 more in a brand store that buy ing in a normal store.

step-by-step explanation:

brand = spend   $ 135.85 total

store = spend $80.07 total

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4