Question

In a study to establish the absolute threshold of hearing, 80 male college freshmen were each seated in a soundproof room and a 150 H tone was presented at a large number of stimulus levels in a randomized order. The student was asked to press a button if he detected the tone; the experimenter recorded the lowest stimulus level at which the tone was detected. The mean for the group was 22.2 dB with s = 2.1. Estimate the mean absolute threshold for all college freshmen. dB Calculate the 95% margin of error (in dB). (Round your answer to two decimal places.) dB

Answer 1

Answer:

Step-by-step explanation:

Hello!

To study the threshold of hering the researcher took a random sample of 80 male college freshmen.

The students underwent an audiometry test where a tome was played and they had to press a button when they detected it.  The researcher recorded the lowest stimulus level at which the tone was detected obtaining a sample mean of X[bar]= 22.2 dB and a standard deviation of S= 2.1 dB

To estimate the population mean, since we don't have information about the variable distribution but the sample size is greater than 30, you can use the approximation of the standard normal distribution:

X[bar] ± $Z_{1-\alpha /2} * \frac{S}{\sqrt{n} }$

Where the semiamplitude or margin of error of the interval is:

d= $Z_{1-\alpha /2} * \frac{S}{\sqrt{n} }$

Using a 95% level $Z_{0.975}= 1.965$

d= 1.965 * $\frac{2.1}{\sqrt{80} }$

d= 0.46

The point estimate of the population mean of the threshold of hearing for male college freshmen is X[bar]= 22.2 db

And the estimation using a 95%CI is [21.74;22.66]

I hope this helps!