Question

Many veterinarians use the condition of a cat’s fur as an indicator of the cat’s overall health. Dr. Bob is investigating the healthiness of the coats of fur for cats from a certain population. The healthiness of the cat’s fur is evaluated using a quantitative description analysis (QDA), where a veterinarian uses a standard process to rate the fur from 0 to 100, with higher values indicating healthier furs. A sample of 57 cats is selected from this population and is found to have an average QDA score of 50 with a standard deviation of 36, build a 90% confidence interval for the true population mean of the QDA scores. [Round both final answers to one decimal place.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 50

Population standard deviation =    = 36

Sample size = n = 57

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645}

Margin of error = E = Z/2 * ( /n)

= 1.645 * ( 36 /  57 )

= 7.8

At 90% confidence interval estimate of the population mean is,

- E < < + E

50 - 7.8 <   < 50 + 7.8

42.2 <   < 57.8

( 42.2 , 57.8 )

The 90% confidence interval of the true population mean is : ( 42.2 , 57.8 )