Question

Quality Wireless Case

Jackson has collected more samples and is now quite convinced that new daily average hold times follow a Normal distribution with a mean of 79.50 seconds and a standard deviation. He decides to further improve the process in 2006. After ensuring that the revised process is in-control, he collects a new sample of daily average hold times over the first 20 days of January 2006. The average daily hold time for that new sample is 70 seconds with a standard deviation of 12 seconds.

a) If the process had in fact not further improved (i.e. still had a mean of 79.50 seconds and standard deviation of 16.86 seconds), what would be the probability of observing that average of 70 seconds or less for this 20-day sample?
b) Using your answer to a, can you conclude, with a 95% confidence level, that the process improved? Why or why not?

Answer 1

a)

Here we have

μ 79.50. σ 16.86

The z-score for X = 70 is

79.50一一0.56

The probability of observing that average of 70 seconds or less for this 20-day sample is

P(X < 70) P(z <-0.56) 0.2877

b)

Since above probability is greater than 1 - 0.95= 0.05 so we can conclude that the process improved.