Question

In an examination of holiday spending (known to be normally distributed) of a sample of 16 holiday shoppers at a local mall, an average of $54 was spent per hour of shopping. Based on the current sample, the standard deviation is equal to $21. Find a 90% confidence interval for the population mean level of spending per hour

Answer 1

(45.6965,63.2035)

Explanation:

Given that in an examination of holiday spending (known to be normally distributed) of a sample of 16 holiday shoppers at a local mall, an average of $54 was spent per hour of shopping.

i.e.
`\bar x = 54\\ n = 16\\s = 21\\std error = (21)/(√(16) ) \\=5.25`

Margin of error = t critical * std error=9.2035

df = 15

(Here since sample std dev is known we use t critical value)

Confidence interval lower bound =
`54-9.2035 = 45.6965`

Upper bound =
`54+9.2035=63.2035`