n farmers are reportedly struggling in the drought conditions- with the price of
ID: 3069830 • Letter: N
Question
n farmers are reportedly struggling in the drought conditions- with the price of feed so high many have forced to sell up their cattle. John, who represents the farmers, decides to investigate the prices of feed farmers are paying out per week. He finds that from a randomly selected group of 80 farmers, on average they are paying $8000 per week with a standard deviation of $2000. a) b) c) Create a 95% confidence interval for the mean amount of money farmers are paying per week. Explain in context what your interval means. Perform a hypothesis test to find out if the mean amount of money paid out for feed per week is significanthy different to the average of $7000 per week being declared in the media. Use a significance level of 5% and give your conclusion. (3+1+5 9 marks]Explanation / Answer
a)
CI for 95%
n = 80
mean = 8000
z-value of 95% CI = 1.9600
std. dev. = 2000
SE = std.dev./sqrt(n) = 223.60680
ME = z*SE
= 1.96*223.6068
= 438.2613
Lower Limit = Mean - ME = 7561.73873
Upper Limit = Mean + ME = 8438.26127
95% CI (7561.7387 , 8438.2613 )
b)
The above confidence interval indicates that if another sample of 80 farmers is chosen, we are 95% confident that the mean price of cattle feed for the sample lies in the interval
c)
Using the above CI we can perform the hypothesis test
the hypothesized value of 7000 does not fall within the CI
Hence we reject the null hypothesis that mu = 7000
There are significant evidence that the mean price of the cattle feed is different than $7000 per farmer
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