Question

The foreman in the welding department wanted to know what value of allowance to use for a particular section of the shop. A work sampling study was authorized. Only two activity categories were considered: (1) welding and other productive work, (2) personal time, rest breaks, and delays. Over a four week period (40 hours/week), 125 observations were made at random times. Each observation captured the category of activity of each of eight welders in the shop section of interest. Results indicated that category 2 constituted 33% of the total observations. (a) Define the limits of a 96% confidence interval (SD

Answer 1

The answer is "0.3605".

Explanation:

Through 8 welds, every welder have 125 measurements, that overall amount of measurements.

N= 125(8) = 1000

The 96 percent level of trust

`Z_{(\alpha)/(2)} =2.05\\\\\hat{\sigma}_(p) = \sqrt{(0.33 (0.67))/(1000)}\\\\`

`=\sqrt{ (0.2211)/(1000)}\\\\=√(0.0002211)\\\\=0.01487`

`\hat{P_2} - Z_{(\alpha)/(2)} \hat{\sigma}_(p) = 0.33 -2.05 (0.01487)\\\\`

`= 0.33-0.0305\\\\=0.2995`

`\hat{P_2} + Z_{(\alpha)/(2)} \hat{\sigma}_(p) = 0.33 +2.05 (0.01487)`

`= 0.33+0.0305\\\\=0.3605`