# Statistical analysis: standard deviation

1. A researcher is interested in estimating the noise levels in decibels at area urban hospitals. She wants to be 90% confident that her estimate is correct. If the standard deviation is 4.13, how large a sample is needed to get the desired information to be accurate within 0.68 decibels?

2. Assume that the population of heights of male college students is approximately normally distributed with mean m of 73.63 inches and standard deviation s of 6.73 inches. A random sample of 97 heights is obtained.

(a) Find the mean and standard error of the x bar distribution

(b) Find P(x bar > 73.50)

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1. A researcher is interested in estimating the noise levels in decibels at area urban hospitals. She wants to be 90% confident that her estimate is correct. If the standard deviation is 4.13, how large a sample is needed to get the desired information to be accurate within 0.68 decibels? Show all work.

Answer

The minimum sample size is given by the formula

Given that ...

#### Solution Summary

The statistical analysis for standard deviations are examined.

BIOSTATISTICS

2.A group of 25 subjects have their diastolic blood pressures measured. The results, in SPSS are:

|-----------|-------|--------|

|N |Valid |25 |

|-------|--------|

| |Missing|0 |

|-----------|-------|--------|

|Median |85.00 |

|-------------------|--------|

|Mode |82.00 |

|-------------------|--------|

|Minimum |55.00 |

|-------------------|--------|

|Maximum |110.00 |

|-----------|-------|--------|

|Percentiles|25 |71.00 |

| |-------|--------|

| |50 |85.00 |

| |-------|--------|

| |75 |98.00 |

|--------|-------|--------|

Don't worry about values exactly at the endpoints of these intervals. Do the calculations roughly.

(1 point each)

a. What percentage of subjects were from 55 to 85?

b. What percentage of subjects were < 85?

c. What percentage of subjects were from 71 to 85?

d. What percentage of subjects were > 71?

e. What percentage of subjects were > 98?

f. Is there one value more common than the rest, and if so, what is it?

3. Assume you have already been give a Z value. This saves you a step. Consider and determine the following probabilities (1 point each).

A. Pr (-1 < Z < 1)

B. Pr (0 < Z < 1)

C. Pr (Z > 1)

D. Pr (-1 < Z < 0)

E. Pr (Z < -1)

F. Pr (Z > -2)

G. Pr (-1 < Z < 2)

4. Suppose the mean systolic blood pressure in a group of individuals is 150 mmHg, with a standard deviation of 15. Assuming SBP follows a normal distribution in this population, compute (1 point each):

A. Pr (135 < value < 165)

B. Pr (value > 165)

C. Pr (value < 135)

D. Pr (138.75 < value < 161.25)

5 Compute the 5th, 50th, and 95th percentiles of SBP from the previous question. (3 points: 1 each).

In questions 6 - 8, use the 1 and 2 SD rules, without the table.

6.In general, what percentage of a Gaussian data set is within 1 SD of the mean? What percentage is within 2 SD's of the mean? (2 points: 1 each)

7.If the mean grade on an exam was 80, SD = 6, where did about 68% of the grades fall? How about 95%? Assume the grades are Gaussian. (2 points).

8.Consider the following data: 1, 1, 2, 2, 4, 5, 6, 9, 40, 200

Use the 68% and 95% rules to test the normality of these data. (2 points).

9.A researcher studying a subtype of lymphocytes obtains a sample mean of 100 per mL, and a standard deviation of 20, with 25 subjects. Within what interval can you be roughly 68% sure the population mean number of these cells per mL lies? How about 95% sure? (2 points)

10.A researcher has a sample of 500 subjects. The mean is 40, median is 20, range 10-100. (2 points each)

a.Could this researcher calculate a useful interval with 95% probability of containing the population mean (using the mean and SEM)? Explain

b.Could the researcher use the mean and SD to usefully estimate where 95% of the individual subject values were? Explain

c)If there were 10 subjects, would your answers to a and b change?

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