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 a 95 percent confidence interval for the mean sensory rate using a given set of data, calculate the sample mean, standard deviation, standard error, and then apply the critical t-value to define the interval, which yields a range of (7.30, 9.15) for this data set.

Step-by-step explanation:

To construct a 95 percent confidence interval for the mean sensory rate for a population from the given sample data, we will follow these steps:

1. Calculate the mean (μ) of the given data.
2. Calculate the standard deviation (s) of the data.
3. Since the sample size (n) is less than 30, use the t-distribution to find the critical t-value for a 95% confidence level.
4. Calculate the standard error (SE) of the mean by dividing s by the square root of n.
5. Construct the confidence interval by adding and subtracting the product of the critical t-value and SE from the sample mean.

Using these steps with the provided data, you will get a confidence interval which estimates that the true population mean sensory rate is between the lower and upper bounds of the interval. Doing so with the given data predicts a 95 percent confidence interval of (7.30, 9.15).