1. A furniture company wants to test a random sample of sofas to determine how long the cushions last. They simulate people sitting on the sofas by dropping a heavy object on the cushions until they wear out; they count the number of drops it takes. This test involves 9 sofas.

• Mean = 12,648.889
• s = 1,898.673

  Assume it follows a normal distribution. Generate a 95% confidence interval for this problem. Remember to use a t-value. Label all the parts.

2. The data below are a random sample of 30 observations drawn from a population that is distributed normally with μ = 75 and σ = 8. Sampling theory tells us that most of the confidence intervals constructed from samples drawn randomly from a population contain the true population value. Check this with this sample, since we know the true population value.

Mean = 76.01

Std Dev = 6.48

n = 30.00

• Construct a 95% confidence interval around the mean using σ = 8. Since sigma is known, use a z-value from the standard normal distribution. For the confidence interval, show the estimate, the z-value, the bound of error (BOE), and the lower and upper values of the confidence interval.
• Describe the confidence interval in words. Did the interval contain the population value of 75?
• Construct the same 95% confidence interval, but use the sample estimate of the standard deviation and a t-value to construct the confidence interval. Compare this result with the interval constructed in the first part.