Answer: [tex]CI\text{ = 59 }\pm\text{ 3.35 ounces}[/tex]
Explanation:
Given:
number of turtles = 42
mean weight = 59 ounces
Population standard deviation = 13.2 ounces
To find:
To construct a 90% confidence interval for the true population mean
To get the confidence interval, we will apply the formula:
[tex]\begin{gathered} CI\text{ = mean }\pm\text{ Z}_{90\text{ \%}}\times\frac{\sigma}{\sqrt{n}} \\ \sigma\text{ = standard deviation} \\ n\text{ = number of sample} \end{gathered}[/tex]
Z score for 90% confidence interval = 1.645
[tex]\begin{gathered} CI\text{ = 59 }\pm1.645\times\frac{13.2}{\sqrt{42}} \\ \\ CI\text{ = 59 }\pm\text{ 1.645\lparen2.0368\rparen} \end{gathered}[/tex][tex]\begin{gathered} CI\text{ = 59 }\pm\text{ 3.350536} \\ \\ CI\text{ = 59 }\pm\text{ 3.35 ounces \lparen2 decimal place\rparen} \end{gathered}[/tex]
