Question

A certain commodity is known to have a price that is stable through time and does not change according to any known trend. Price, however, does change from day to day in a random fashion. If the price is at certain level one day, it is as likely to be at any level the next day within some probability bounds approximately given by a normal distribution. The mean daily price is believed to be $14.30. To test the hypothesis that the average price is $14.30 versus the alternative hypothesis that it is not $14.30, a random sample of 16 daily prices is collected. The results are           x-bar=$16.48 and s=$5.82. Using ?=0.05, can you reject the null hypothesis?

Answer 1

Null Hypothesis : Mean of sample is $ 14.30

Alternative Hypothesis:Mean of samples is not $ 14.30

Mean of population = $ 14.30

X-bar = $ 16.48

s =$ 5.82

= ( $ 16.48 - $ 14.30 ) / $ 5.82

= $ 2.18 / $ 5.82

= 0.3745

As this is the case of two tail, we will find the probability value when z = 0.3745

When, we look in Z-table, we find probability value = 0.32

Alpha-value = 0.05

When probability value is greater than alpha, we do not reject null hypothesis