Question

The pulse rates of 155 randomly selected adult males vary from a low of 41 bpm to a high of 109 bpm. Find the minimum sample size required to estimate the mean pulse rate of adult males. Assume that we want 90% confidence that the sample mean is within 2 bpm of the population mean. Complete parts (a) through (c) below.
a. Find the sample size using the range rule of thumb to estimate σ n= Type a whole number.,) (Type a whole number.)
b. Assume that σ = 11.6 bpm, based on the value s = 11.6 bpm from the sample of 155 male pulse rates. n= (Type a whole number.)
c. Compare the results from parts (a) and (b). Which result is likely to be better?
The result from part (a)_________the result from part (b). The result from______is likely
larger than
smaller than
the same
size as

Answer 1

Answer:

Part (a): 194; part (b): 90 and part (c): larger than

Step-by-step explanation:

Part (a): Range is 109-41 = 68

Std. deviation = range/4 = 68/4 = 17

For n, Error (E) = z of 90%*std. dev/$\sqrt{x}$n

So n = (z of 90%*std. dev/E)^square...(i)

Z value for 90% confidence = 1-alpha = 0.90

alpha = 0.1

We take alpha/2 for z value calculation, so 0.1/2 is 0.05. Look up the z table and you get 1.64.

Going back to equation (i),

n = (z of 90%*std. dev/E)^square = (1.64*17/2)^square = 194.32 = 194

N must be a whole number that is why we have approximated it to 194.

Part (b): Put given values in equation (i)

n = (z of 90%*std. dev/E)^square = (1.64*11.6/2)^sqaure = 90.478 =90.5 = 90

0.5 is rounded down if the number on the left is an even number and is rounded up when the number on the left is odd. Here, 90 is an even number so we rounded down.

Part (c): The result from part (a)_________the result from part (b).

Since, 194 is 'larger than' 90 hence, result from part (a) is larger than the result from part (b). Also, result form part (a) is likely to be better as larger sample size gives more reliable results.

Answer 2

Based on the range rule of thumb, the sample size is equal to 194.

Given the following data:

• Population = 155 adult males.

• Low rate = 41 bpm.

• High rate = 109 bpm.

• Sample mean = 2 bpm.

• Confidence interval = 90%.

How to calculate the sample size.

First of all, we would determine the range and then use the range rule of thumb to estimate the standard deviation:

Note: Range represents the minimum and maximum value of a data set.

Range = $109-41$

Range = 68.

For the standard deviation:

$\delta =\frac{Range}{4} \\\\\delta =\frac{68}{4}$

Standard deviation = 17.

At 90% confidence interval, we have;

$0.90=1-\alpha \\\\\alpha =1-0.90\\\\\alpha =0.10\\\\\\Z=\frac{\alpha}{2} \\\\Z =\frac{0.10}{2} \\\\Z =0.05$

From the z-table, we have;

Z-score = 1.64

Error = 2.

$Error =Z_o\times \frac{\delta}{\sqrt{n} } \\\\\sqrt{n} =Z_o\times \frac{\delta}{E}\\\\n=(Z_o\times \frac{\delta}{E})^2\\\\n=(1.64 \times \frac{17}{2})^2\\\\n=(13.94)^2$

Sample size, n = 194.32 ≈ 194.

Part b.

When standard deviation = 11.6 bpm;

$Error =Z_o\times \frac{\delta}{\sqrt{n} } \\\\\sqrt{n} =Z_o\times \frac{\delta}{E}\\\\n=(Z_o\times \frac{\delta}{E})^2\\\\n=(1.64 \times \frac{11.6}{2})^2\\\\n=(9.512)^2$

Sample size, n = 90.48 ≈ 90.

Part c.

Based on the calculations, the result from part (a) is larger than the result from part (b). Also, the result form part (a) is likely to be better because larger sample size gives more reliable results.

Read more on z-scores here: https://brainly.com/question/4302527