Question

Order in choice. Does the order in which wine is presented make a difference? Several choices of wine are presented one at a time and in sequence and the subject is then asked to choose the preferred wine at the end of the sequence. In this study, subjects were asked to taste two wine samples in sequence. Both samples given to a subject were the same wine, although subjects were expecting to taste two different samples of a particular variety. Of the 32 subjects in the study, 22 selected the wine presented first, when presented with two identical wine samples.(a)Although the conditions for the large-sample test were met in Exercise 22.39, show that the conditions for the large-sample confidence interval discussed in this chapter are not met.(b)Are the conditions for the use of the plus four confidence interval met? If so, use the plus four method to give a 90% confidence interval for the proportion of subjects who would select the first choice presented.

Answer 1

A)The conditions are not met on the grounds that utility determined decreases with increment in utilization. A significant number of them chose the primary wine in light of the fact that, the fulfillment got from the main wine was higher, and it diminishes as their beverage a greater amount of the wine.

b)The state of the utilization of in addition to is met in light of the fact that the certainty interim must be more prominent than zero, so the in addition to part of the equation met the criteria.

The certainty interim for the individuals that choosed the main wine is from 21 to 23.

Refer below for the explanation.

Explanation:

Calculations,

90% confidence interval.

Therefore;

0.9 + 1.64(√(0.9(1-0.9)/32)) = 0.99 = 1

Or

0.9 - 1.64(√(0.9(1-0.9)/32)) = 0.813

Answer 2

a) The conditions are not met because utility derived reduces with increase in consumption. Many of them selected the first wine because, the satisfaction derived from the first wine was higher, and it reduces as their drink more of the wine.

b)The condition of the use of plus is met because the confidence interval has to be greater than zero, so the plus aspect of the formula met the criteria.

The confidence interval for the people that choosed the first wine is from 21 to 23

Explanation:

A confidence interval is the amount of uncertainty in the e result of a sample population

This is calculated using

P + z(√(p(1-p)/n)) or p - z(√(p(1-p)/n))

P is the proportion 90%

Z is a constant gotting from a confidence level table. At 90% Z is 1.64

Therefore;

0.9 + 1.64(√(0.9(1-0.9)/32)) = 0.99 = 1

Or

0.9 - 1.64(√(0.9(1-0.9)/32)) = 0.813

Because the confidence interval should be a greater than zero, the positive sign is the best equation for this.

Therefore the confidence interval is

22 + 1 or 22 - 1

Which is from 21 to 23