The branch manager of an outlet of a nationwide chain of pet supply stores wants to study characteristics of her customers. In particular, she decides to focus on two variables: the amount of money spent by customers and whether the customers own only one dog, only one cat, or more than one dog and/or cat. The results from a sample of 70 customers are follows:

- Amount of money spent: X = $21.34, S=$9.22
- 37 customers own only a dog
- 26 customers own only a cat
- 7 customers own more than one dog and/or cat

a) Construct a 95% confidence interval estimate of the population mean amount in the pet supply.
b) Construct a 90% confidence interval estimate of the population proportion of customers who own only a cat

No results were presented

a) To construct a confidence interval estimate of the population mean amount in the pet supply, we can use the following formula:

CI = X ± Z * (S / √n)

Where:
X = Sample mean amount of money spent
Z = Z-score corresponding to the desired level of confidence (95% confidence level corresponds to Z = 1.96)
S = Sample standard deviation
n = Sample size

Given:
X = $21.34
S = $9.22
n = 70
Z = 1.96 (for 95% confidence level)

Calculating the confidence interval using the formula, we have:

CI = $21.34 ± 1.96 * ($9.22 / √70)

CI = $21.34 ± 1.96 * ($1.104)

CI = $21.34 ± $2.163

So, the 95% confidence interval estimate of the population mean amount in the pet supply is $19.17 to $23.51.

b) To construct a confidence interval estimate of the population proportion of customers who own only a cat, we can use the following formula:

CI = p ± Z * √[(p * (1-p)) / n]

Where:
p = Sample proportion
Z = Z-score corresponding to the desired level of confidence (90% confidence level corresponds to Z = 1.645)
n = Sample size

Given:
p = 26/70 = 0.371 (proportion of customers who own only a cat)
Z = 1.645 (for 90% confidence level)
n = 70

Calculating the confidence interval using the formula, we have:

CI = 0.371 ± 1.645 * √[(0.371 * (1-0.371)) / 70]

CI = 0.371 ± 1.645 * √[(0.233 * 0.629) / 70]

CI = 0.371 ± 0.153

So, the 90% confidence interval estimate of the population proportion of customers who own only a cat is 0.218 to 0.524.