# The proportion of defective computers built by byte

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: The proportion of defective computers built by Byte Computer Corporation with new assembly process is 0 . 15. H 1 : The proportion of defective computers built by Byte Computer Corporation with new assembly process is lower than 0 . 15. H 0 : p = 0 . 15 vs H 1 : p < 0 . 15 The test statistics is z = ˆ p - p 0 q p 0 (1 - p 0 ) n z = 0 . 095 - 0 . 15 q 0 . 15 0 . 85 42 = 0 . 995 . p - value = P [ Z < - 0 . 995] = . 1587 Since p - value > 0 . 01 ( or the test statistic Z = - . 995 is greater than - z 0 . 01 = - 2 . 33) we fail to reject the null hypothesis. Therefore, we cannot conclude that the proportion of defective computers has been lowered. 7. The sample proportion of sailboat owners who used their boats more than 6 times each summer is ˆ p = x/n = 42 / 70 = 0 . 6 . H 0 : the proportion of sailboat owners who use their boats more than 6 times each summer is 0 . 4. H 1 : the proportion of sailboat owners who use their boats more than 6 times each summer is greater than 0 . 4. H 0 : p = 0 . 4 vs H 1 : p > 0 . 4. The test statistics is z = ˆ p - p 0 q p 0 (1 - p 0 ) n z = 0 . 60 . 4 q 0 . 4 0 . 6 42 = 3 . 41 . p - value = P [ Z < - 3 . 41] = 0 . 00325 Since p - value = 0 . 00325 is smaller than = 0 . 005 (or test statistic 3 . 41 is greater than z 0 . 005 = 2 . 575), we reject the null hypothesis and conclude that there is a reason to believe that the proportion of sailboat owners who use their boats more than 6 times each summer is greater than 0.4. 3
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