Question

Suppose you ao a study of acupuncture to determine how effective it is in relieving pain. You measure sensory rates for 15 subjects(; 9.4; 7.9; 6.8; 8.3; 7.3; 9.2; 9.6; 8.7; 11.4; 10.3; 5.4; 8.1; 5.5; 6.9) with the results given. Use the sample data to construct a 95 percent confidence interval for the mean sensory rate for the population (assumed normal) from which you took the data____

Answer 1

To construct the confidence interval, calculate the sample mean and standard deviation, then use the t-distribution to find the t*-value and apply the confidence interval formula. For the given data, the 95% confidence interval for the mean sensory rate is (7.30, 9.15).

Step-by-step explanation:

Constructing a 95% Confidence Interval

To construct a 95 percent confidence interval for the mean sensory rate, you first need to calculate the mean (μ) and standard deviation (s) of the sample data. After that, use the t-distribution since the sample size is less than 30 and we do not know the population standard deviation. You will need the degrees of freedom (df), which is n - 1. With df = 14 for a 95% confidence interval, find the t*-value, which you can look up in a t-table or use a calculator to find.

Now the formula for the confidence interval is:

mean ± (t* × (s / √ n))

Plug in the values for the mean, t*, s (sample standard deviation), and n (sample size) to calculate the interval. For this dataset, the 95% confidence interval for the mean sensory rate is (7.30, 9.15).

This means we estimate with 95 percent confidence that the true population mean sensory rate is between 7.30 and 9.15.