Some people claim that women can experience “mother hearing”, an increased sensi

Question

Some people claim that women can experience “mother hearing”, an increased sensitivity to and awareness of noises, in particular those of children. This special ability is often associated with being a mother, rather than simply being female. Below are some hypothetical data where we recruited women to come to a sleep experiment where they think they are evaluating the comfort of different mattresses. While they are asleep, we introduce noises to test the minimum volume needed for the women to be awakened by the noise. The data are in decibels (dB). Do the data indicate as significant difference in sensitivity to noise between mothers and non-mothers? State the null hypothesis, use a two-tailed test with = .05, include r2 in the event that you reject H0, and conclude with an appropriate summary statement.

Mothers 33 45 39 41 47

Non Mothers 56 48 71

Explanation / Answer

Solution:

Here, we have to use two sample t test for the population mean.

H0: µ1 = µ2 versus H0: µ1 µ2

We are given

Level of Significance

0.05

From the given observations we have

Population 1 Sample

Sample Size

5

Sample Mean

41

Sample Standard Deviation

5.4772

Population 2 Sample

Sample Size

3

Sample Mean

58.33333333

Sample Standard Deviation

11.6762

Degrees of Freedom

6

Test statistic formula is given as below:

t = (X1bar – X2bar) / sqrt[(S1^2/N1)+(S2^2/N2)]

t = (41 – 58.33) / sqrt[(5.48^2/5)+(11.68^2/3)]

t = -2.4166

P-value = 0.0521

= 0.05

P-value >

So, we do not reject the null hypothesis

We conclude that there is insufficient evidence that the data indicate a significant difference in sensitivity to noise between mothers and non-mothers.

Level of Significance

0.05

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