( c ) ( i ) Write down the null hypothesis of the test .
( ii ) Write down the alternative hypothesis of the test .
( iii ) Find the p -value .
( iv ) State the conclusion of the test with a reason .
[ 6 ] Lucy wants to conduct another hypothesis test at a certain significance level to test whether the population mean weight of oranges is less than 120 g . She chooses rejecting the null hypothesis if the sample mean is less than 119.2 g . The sample size used is 21 .
( d ) Find the probability that a Type I error is made .
The actually value of � is 119.6 .
[ 2 ]
( e ) Find the probability that a Type II error is made .
Later , Lucy takes another random sample of n oranges to calculate a 90 % confidence interval for � . It is given that the upper bound of the confidence interval is 1.6449v greater than the sample mean weight , where v is the standard deviation of the sample mean weight .
( f ) ( i ) Express v in terms of n .
[ 2 ]
( ii ) Hence , find the least value of n such that the width of the confidence interval is not greater than 1.1 grams .
[ 6 ]
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