Answer to Question #346864 in Statistics and Probability for Yanna

Question

A company manufactures a new type of mosquito repellents with the period of effectiveness that is approximately normally distributed with a standard deviation of 30 hours. A sample of 40 repellents was taken and the average period of effectiveness is 290 hours. Calculate a 96% confidence interval for the true mean of the period of effectiveness

Answer 1

The critical value for $\alpha = 0.04$ is $z_c = z_{1-\alpha/2} = 2.0537.$

The corresponding confidence interval is computed as shown below:

$$CI=(\bar{x}-z_c\times\dfrac{\sigma}{\sqrt{n}}, \bar{x}+z_c\times\dfrac{\sigma}{\sqrt{n}})$$

$$=(280.258, 299.742)$$

Therefore, based on the data provided, the 96% confidence interval for the population mean is $280.258 < \mu < 299.742,$ which indicates that we are 96% confident that the true population mean $\mu$ is contained by the interval $(280.258, 299.742).$