# The management of KSmall .pdf - Question The management of...

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Question The management of KSmall Industries is considering a new method of assembling a computer. The current assembling method requires a mean time of 60 minutes with a standard deviation of 2.7 minutes. Using the new method, the mean assembly time for a random sample of 24 computers was 58 minutes. Using the .10 level of significance, can we conclude that the assembly time using the new method is faster? What is the probability of a Type II error?
Step 4 The z -test statistics is,
The z -test statistics is . , Step 5 Decision The z value corresponds to sample statistics is falls in the critical region, so the null hypothesis is rejected at 10% level of significance. There is sufficient evidence to indicate that the new method is faster than 60 minutes. The result is statistically significant. , Step 6 The probability of Type II error ( ) is, The critical value for left-tailed is, , Step 7 The critical value for left-tailed is 59.29. , Step 8 The probability of sample mean 58 and 59.29 between is, For converts to For converts to
, Step 9 From the standard normal distribution table, the associated probability for z values and subtracts the probability is, The probability of sample mean 58 and 59.29 between is0.4904. , Step 10 The probability of Type II error ( ) is, The probability of Type II error ( ) is .