A marketing team wants to estimate the average customer satisfaction score for a new product. A random sample of 20 customers is selected, and their satisfaction scores (on an increasing satisfaction scale of 1 to 10) are recorded as follows:
8, 7, 9, 6, 8, 7, 6, 9, 10, 8, 7, 6, 9, 8, 7, 8, 9, 6, 8, 7
Assuming the satisfaction scores are normally distributed, calculate the 90% confidence interval for the average customer satisfaction score for the new product.
Please show all the necessary following steps and provide your answer with the appropriate interpretation.
Calculate the sample mean and sample standard deviation.
Determine the critical value (t-value) for a 90% confidence level.
Calculate the margin of error using the critical value and sample standard deviation.
Calculate the lower and upper bounds of the confidence interval using the sample mean and margin of error.
Interpret the confidence interval in the context of the problem.