Biologists studying the healing of skin wounds measured the rate at which new cells closed a razor cut made in the skin of an anesthetized newt. Here are data from 18 newts, measured in micrometers per hour: 29,27,34,40,22,28,14,35,26,35,12,30,23,18,11,22,23,33.

Questions: a)Scientists usually assume that animal subjects are SRSs from their species or genetic type. Treat these newts as an SRS and suppose you know that the standard deviation of healing rates for this species of newt is 8 micrometers per hour. Give a 90% confidence interval for the mean healing rate for the species.

First, calculate the mean of the 18 observations. You are given the SD at 8. Use a cumulative normal distribution table (probably in the back of your stats text). Find the appropriate factor for a 90% confidence interval (hint: your interval should reflect a 2-tailed test). Call this factor U. 90% confidence would be (mean - 8*U) to (mean + 8*U)

Mean = 26.7

U = 1.645

90% confidence interval for the mean healing rate for the species is (20.9, 32.5).

To calculate the mean of the 18 observations, add up all the values and divide by the total number of observations:

29 + 27 + 34 + 40 + 22 + 28 + 14 + 35 + 26 + 35 + 12 + 30 + 23 + 18 + 11 + 22 + 23 + 33 = 492

Mean = 492 / 18 = 27.33

Next, determine the appropriate factor for a 90% confidence interval. Since it's a 2-tailed test, we need to find the z-score that corresponds to a cumulative probability of 0.05 (0.1/2) in the tails of the standard normal distribution.

Using a standard normal distribution table, we find that the z-score corresponding to a cumulative probability of 0.05 is approximately 1.645.

Now we can calculate the confidence interval:

Lower bound = mean - (8 * U)
Upper bound = mean + (8 * U)

Lower bound = 27.33 - (8 * 1.645) = 27.33 - 13.16 ≈ 14.17
Upper bound = 27.33 + (8 * 1.645) = 27.33 + 13.16 ≈ 40.49

Therefore, the 90% confidence interval for the mean healing rate for the species is approximately 14.17 to 40.49 micrometers per hour.

To calculate the mean healing rate for the species and obtain a 90% confidence interval, you need to follow these steps:

1. Calculate the mean of the 18 observations. Add up all the data points and divide by the total number of observations (18 in this case). The mean, denoted as μ, would be the sum of the data divided by 18.

2. Find the appropriate factor for a 90% confidence interval. This factor can be obtained from a cumulative normal distribution table (also known as a Z-table). For a 90% confidence interval, you need to find the value that corresponds to an area of 0.05 in each tail of the distribution. In a standard normal distribution, this value is approximately 1.645.

3. Calculate the margin of error. The margin of error is determined by multiplying the standard deviation (given as 8 micrometers per hour) by the factor obtained in step 2. In this case, the margin of error would be 8 * 1.645.

4. Finally, construct the 90% confidence interval. Subtract the margin of error from the mean to get the lower bound of the interval and add the margin of error to the mean to get the upper bound of the interval. This gives you the 90% confidence interval for the mean healing rate of the species.

So, the 90% confidence interval would be (mean - 8 * 1.645) to (mean + 8 * 1.645). Plug in the calculated values to obtain the final interval.