The mean retail price for bananas in 1994 was 460 cents per

The mean retail price for bananas in 1994 was 46.0 cents per pound. Currently, a random sample of 15 markets gave a mean price of 48.4 cents per pound with a standard deviation of 3.5 cents.

a. Identify the variable in this set up

b. Identify an individual in this set up

c. Assuming that the retail price of bananas is normally distributed, is there enough evidence at = 0.05 level of significance to conclude that the current mean retail price of bananas has increased sinc

Solution

a) Here the random variable is the mean retail price for bananas.

b) An individual is each sample mean calculated from different samples

c. Set null and alternate hypotheses as:

H0: mu = 46

Ha: mu>46

Right tailed test

Sample mean = 48.4

std dev = 3.5

As n = 15, std error of sample = 3.5/rt 14

= 0.9354

Sample mean is normal with (46, 0.9354)

Test statistic t = Mean difference/0.9354 = 2.565

df = 14

p value = 0.0112

As p < 0.05 reject null hypothesis

Conclusion: Mean of bananas have increased from 46.0 and this is statistically evident