Question

A researcher is interested in whether infants’ attention to their mothers’ voices increases in the first week of life. Let’s assume an established baseline exists showing that infants attend to their mothers, on average, for 5.867 seconds on their first day. The researcher selects 15 full-term infants in normal health who experienced uncomplicated deliveries and tests the number of seconds the infants oriented in the direction of their mother’s voice on Day 7 after delivery. Here are the results: 7, 7, 6, 8, 8, 8, 8, 8, 6, 7, 7, 7, 7, 8, 6. Test the hypothesis that attention to the mother’s voice increases over the first 7 days of life, using alpha=.05.

Answer 1

Here claim is infants’ attention to their mothers’ voices increases in the first week of life.

Which means mean is greater than 5.867

So hypothesis is vs

Now for given data mean value is

Create the following table.

data	data-mean	(data - mean)2
7	-0.2	0.04
7	-0.2	0.04
6	-1.2	1.44
8	0.8	0.64
8	0.8	0.64
8	0.8	0.64
8	0.8	0.64
8	0.8	0.64
6	-1.2	1.44
7	-0.2	0.04
7	-0.2	0.04
7	-0.2	0.04
7	-0.2	0.04
8	0.8	0.64
6	-1.2	1.44

Find the sum of numbers in the last column to get.

So

Let us assume that distribution is normal

So test statistics is

So P value is TDIST(6.66,14,1)=0.0000

As P value is less than alpha, we reject the null hypothesis

Hence we have sufficient evidence to support the claim that infants’ attention to their mothers’ voices increases in the first week of life