Georgianna claims that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons. we have a random sample of 20 children from the city, with a mean of 4.6 years of piano lessons and a standard deviation of 2.2 years. what is the 90% confidence interval for the average number of years students take piano lessons in this city?

Step-by-step explanation:

Given : Sample size of  children : n= 20

Degree of freedom = df =n-1 =20-1=19

Sample mean years of piano lessons :

Sample standard deviation :

Confidence level :

Significance level :

Since population standard deviation is unavailable, then

Confidence interval for the population mean :

 (1)

Using t-distribution table , we have

Critical value =

The 90% confidence interval for the average number of years students take piano lessons in this city will be :

 (Substitute the values in (1))

Hence, the 90% confidence interval for the average number of years students take piano lessons in this city =