California Innovations

Help with confidence intervals, please.?

In an article in the Journal of Management, Morris, Avila and Allen studied innovation by surveying firms to find the number of new products introduced by the firms. A randon sample of 100 California firms are selected. Each firm is asked to report the number of new products introduced last year. The survey found that on average, these firms introduced 5.68 products with a standard deviation of 8.70. Compute a 98% confidence interval for the new products introduced last year.

The formula for a confidence interval:

CI = xbar ± z * (s / sqrt(n))
where:
CI = Confidence Interval
xbar = sample mean (5.68)
s = sample standard deviation (8.70)
n = number of observations (100)
z = 2.325 (from table lookup)

Since n > 30, we assume a normal distribution and the sample standard deviation can be substituted for the population standard deviation. (This means using a z-test instead of a t-test).

The confidence interval is :
CI = xbar ± z * (s / sqrt(n))
CI = 5.68 ± 2.325 * (8.70 / sqrt(100))
CI = 5.68 ± 2.325 * (8.70 /10)
CI = 5.68 ± 2.325 * (.87)
CI = 5.68 ± 2.02
CI = 3.66 to 7.70

Good luck in your studies,
~ Mitch ~

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