Answer :
Answer:
The 99% confidence interval for the population mean is 22.96 to 26.64
Step-by-step explanation:
Consider the provided information,
A sample of 49 customers. Assume a population standard deviation of $5. If the sample mean is $24.80,
The confidence interval if 99%.
Thus, 1-α=0.99
α=0.01
Now we need to determine [tex]z_{\frac{\alpha}{2}}=z_{0.005}[/tex]
Now by using z score table we find that [tex]z_{\frac{\alpha}{2}}=2.58[/tex]
The boundaries of the confidence interval are:
[tex]\mu-z_{\frac{\alpha}{2}}\times \frac{\sigma}{\sqrt{n} }\\24.80-2.58\times \frac{5}{\sqrt{49}}=22.96\\\mu+z_{\frac{\alpha}{2}}\times \frac{\sigma}{\sqrt{n} }\\24.80+2.58\times \frac{5}{\sqrt{49}}=26.64[/tex]
Hence, the 99% confidence interval for the population mean is 22.96 to 26.64