Question

A string quartet in Maui wants to better understand its income stream, which primarily comes from playing at weddings. The cellist records the number of weddings the quartet plays in six successive months. Construct a 90% confidence interval from her results: 3, 5, 7, 4, 4, and 5.

a) 3.2 to 5.8
b) 4.0 to 5.6
c) 3.7 to 5.3
d) 4.2 to 5.4
e) 3.5 to 5.7

Answer 1

To construct a 90% confidence interval for the income stream of the string quartet, use the formula Confidence Interval = sample mean ± (critical value * standard error).

Step-by-step explanation:

To construct a 90% confidence interval for the income stream of the string quartet, we can use the formula:

Confidence Interval = sample mean ± (critical value * standard error)

From the given data, the sample mean is 4.67 and the standard deviation is 1.53. The critical value can be found using a t-distribution table for a 90% confidence level with 5 degrees of freedom (n - 1).

Using the t-distribution table, the critical value is approximately 2.015. Therefore, the 90% confidence interval is:

(4.67 - (2.015 * 1.53), 4.67 + (2.015 * 1.53))

Simplifying the calculation, the 90% confidence interval is approximately:

(3.13, 6.21)