[Remoo]

The owner of a petrol station wants to study fuel-purchasing habits of motorists at his
station. A random sample of 60 motorists during a particular week gave the following
results:
Amount purchased: x = 42.8 litres, S =11.7 litres.
9 motorists purchased diesel.

Set up a 95% confidence interval estimate for the proportion of motorists who buy
diesel. Write a sentence to explain the meaning of your answer.
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Hello Guys, I have this Question for stats that I am really stuck on, what I have already wrote for this is:

Answer: z_c = 1.96

margin of error, E = (S*z_c)/sqrt(n)
= (11.7*1.96)/sqrt(9)
= 7.644

95% CI = (x-bar - E, x-bar +E)
= (42.8 - 7.644, 42.8 + 7.644)
= (35.156, 50.444) (Ans.)
this is what I wrote.

also it has 2 more sub questions and they are as follows

Test at the 5% level whether there is evidence that the mean amount purchased is more than 40 litres.


Before carrying out the survey, the owner thought that 10% of his customers used diesel. Do the results of the survey suggest that he was wrong? Explain.


if any one is able to help me, I would be greatly appreciated.
Kind Regards