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Chapter 6, Section 2-CI, Exercise 091 How Many Birds Do Domestic Cats Kill? "Domestic cats kill many more wild birds in the United States than scientists thought," states a recent article. 1 Researchers used a sample of n = 140 households in the US with cats to estimate that 35% of household cats in the US hunt outdoors. A separate study2 used kittyCams to record all activity of n 55 domestic cats that hunt outdoors. The video footage showed that the mean number of kills per week for these cats was 2.4 with a standard deviation of 1.51. Find a 90% confidence interval for the mean number of kills per week by US household cats that hunt outdoors. Round your answers to three decimal places.

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JeanaShupp

Answer: [tex](2.065,\ 2.735)[/tex]

Step-by-step explanation:

The confidence interval for population mean is given by :-

[tex]\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}[/tex]

Given : Significance level : [tex]\alpha: 1-0.9=0.1[/tex]

Critical value : [tex]z_{\alpha./2}=1.645[/tex]

Sample size : [tex]n=55[/tex]

Sample mean : [tex]\overline{x}=2.4[/tex]

Standard deviation : [tex]\sigma = 1.51[/tex]

The 90% confidence interval for the mean number of kills per week will be  :-

[tex]2.4\pm (1.645)\dfrac{1.51}{\sqrt{55}}\\\\\approx2.4\pm0.335\\\\=(2.4-0.335,\ 2.4+0.335)=(2.065,\ 2.735)[/tex]

Hence, the 90% confidence interval for the mean number of kills per week by US household cats that hunt outdoors = [tex](2.065,\ 2.735)[/tex]