You measure 46 textbooks' weights, and find they have a mean weight of 73 ounces. Assume the population standard deviation is 6.6 ounces. Based on this, construct a 99% confidence interval for the true population mean textbook weight.
Give your answers as decimals, to two places
To construct a 99% confidence interval for the true population mean textbook weight, we can use the formula:
Confidence Interval = sample mean ± (critical value * standard error)
First, we need to find the critical value for a 99% confidence level. Since the sample size is relatively large (46 textbooks) and the population standard deviation is known, we can use a z-distribution.
The critical value for a 99% confidence level from a z-distribution is approximately 2.58 (you can find this value using a z-table or calculator).
Next, we need to calculate the standard error, which is the standard deviation of the sample mean:
Standard Error = population standard deviation / square root of sample size
Standard Error = 6.6 / √46 ≈ 0.9724
Now, we can construct the confidence interval:
Confidence Interval = 73 ± (2.58 * 0.9724)
Lower bound = 73 - (2.58 * 0.9724) ≈ 73 - 2.51 ≈ 70.49
Upper bound = 73 + (2.58 * 0.9724) ≈ 73 + 2.51 ≈ 75.51
Therefore, the 99% confidence interval for the true population mean textbook weight is approximately 70.49 ounces to 75.51 ounces.