Exercise 78
1 . A die is tossed for 840 times . From the observation , 99 results are shown as ‘ 1 ’ s .
A hypothesis test is conducted at a 1 % significance level to test whether the die is biased such that the probability of getting a ‘ 1 ’ is less than 0.15 .
( a ) ( i ) Write down the null hypothesis of the test .
( ii ) Write down the alternative hypothesis of the test .
( b ) Find the p -value .
( c ) State the conclusion of the test with a reason .
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2 . The number of phone calls received by a customer service counter per hour follows a Poisson distribution with mean � . In a particular hour , there were 13 phone calls .
A hypothesis test is conducted at a 5 % significance level to test whether � is greater than 10 .
( a ) ( i ) Write down the null hypothesis of the test .
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( ii ) Write down the alternative hypothesis of the test .
( b ) Find the p -value .
( c ) State the conclusion of the test with a reason .
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3 . The number of defective items of a supply chain is studied . A sample of 100 items are selected and n items are found to be defective .
A hypothesis test is conducted at a 5 % significance level to test whether the proportion of defective items is greater than 0.03 .
( a ) ( i ) Write down the null hypothesis of the test .
( ii ) Write down the alternative hypothesis of the test . [ 2 ] www . seprodstore . com
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