A purchasing agent wants to estimate the mean daily usage of rye flour. She takes a sample for 50 straight days and find that the sample mean is 180 lbs with a sample standard deviation of 38.5 lbs. a)State the 90% confidence interval for the mean.b) State the margin of error
Use a confidence interval formula:
CI90 = mean ± 1.645(sd/√n)
...where ± 1.645 represents the 90% confidence interval using a z-table, sd = standard deviation, √ = square root, and n = sample size.
Plug your data into the formula to calculate the confidence interval and the margin of error.
I hope this will help get you started.
To find the population mean with a confidence interval, you can use the formula:
Confidence Interval = Sample Mean ± Margin of Error
a) To calculate the 90% confidence interval for the mean daily usage of rye flour:
Step 1: Determine the Z-score for a 90% confidence level. The Z-score associated with a 90% confidence level is 1.645.
Step 2: Calculate the margin of error using the formula:
Margin of Error = Z * (Sample Standard Deviation / √Sample Size)
In this case, the sample mean is 180 lbs, the sample standard deviation is 38.5 lbs, and the sample size is 50.
Margin of Error = 1.645 * (38.5 / √50)
Step 3: Calculate the confidence interval:
Confidence Interval = Sample Mean ± Margin of Error
Confidence Interval = 180 ± Margin of Error
b) To find the margin of error, use the formula mentioned in Step 2:
Margin of Error = 1.645 * (38.5 / √50)
Calculating the above expression will give you the margin of error.