Question

Based on studies conducted in various regions across the country, the average cost of pumpkins for consumers is $3.18 per kg.
From a random sample of 15 farmer’s markets in the Montreal-area you determine that the average price for pumpkins is $4.25 per kg with a standard deviation of $1.90 per kg.
a) Determine the minimum sample size necessary to construct a 95% confidence interval with maximal error of E = 0.5 for the mean price of pumpkins
b) Construct a 95% confidence interval for the average price of pumpkins in the Montreal-area and determine if it differs significantly from that of the rest of the country.

Answer 1

Answer on Question #60548 – Math – Statistics and Probability

Question

Based on studies conducted in various regions across the country, the average cost of pumpkins for consumers is $3.18 per kg.

From a random sample of 15 farmer’s markets in the Montreal-area you determine that the average price for pumpkins is $4.25 per kg with a standard deviation of $1.90 per kg.

a) Determine the minimum sample size necessary to construct a 95% confidence interval with maximal error of E = 0.5 for the mean price of pumpkins.

b) Construct a 95% confidence interval for the average price of pumpkins in the Montreal-area and determine if it differs significantly from that of the rest of the country

Solution

a) $E = t_{crit} \frac{s}{\sqrt{n}} \rightarrow n = \left( \frac{t_{crit} s}{E} \right)^2 = \left( \frac{2.145 \times 1.9}{0.5} \right)^2 \approx 66$.

b) $CI = \left( \bar{x} - t_{crit} \frac{s}{\sqrt{n}}, \bar{x} + t_{crit} \frac{s}{\sqrt{n}} \right) = \left( 4.25 - 2.145 \frac{1.9}{\sqrt{15}}, 4.25 + 2.145 \frac{1.9}{\sqrt{15}} \right) =$

$= (3.20, 5.30).$

Average cost of pumpkin ($3.18) does not fall into confidence interval, therefore we can conclude that the average price of pumpkins in the Montreal-area differs significantly from that of the rest of the country.

Answer: a) 6; b) (3.20, 5.30).

www.AssignmentExpert.com