Question

2.   Sensory isolation chambers are used to examine the effects of mild sensory deprivation. The chamber is a dark, silent tank where subjects float on heavily salted water and are thereby deprived of nearly all external stimulation. Sensory deprivation produces deep relaxation and had been shown to produce temporary increases in sensitivity for vision, hearing, touch, and even taste. The following data represent hearing threshold scores for a group of subjects who were tested before and immediately after one hour of deprivation. A lower score indicates more sensitive hearing. Do these data indicate that deprivation has a significant effect on hearing threshold? Test at the .05 level of significance with two tails.

subject	before	after
A	31	30
B	34	31
C	29	29
D	33	29
E	35	32
F	32	34
G	35	28

a)   State symbolically what your H1 and H0 would be.
b)   What kind of test would you use (One-sample, Related-samples, etc.)?
c)   What is your df? What is your critical t?
d)   Based on the above information, would you reject H0, or fail to reject it? Why? What would your conclusion be?

Answer 1

b) See the data collected on same subject ( person ) so it is dependent data

For dependent data set we use pair t test.

Here we want to test "whether the deprivation has a significant effect on hearing threshold or not"

a) Let's write null hypothesis (H₀) and alternative hypothesis(H₁)

Where is the population mean difference of before minus after.

For the answer of part c) and d) let's used excel :

Step 1) Enter the given data in excel columns.

Step 2) Click on Data >>>Data Analysis >>> t-Test: Pair Two sample for Means

then click on OK

In variable 1 Range select data of Before

In variable 1 Range select data of After

Hypothesized mean difference : 0

Select Labels

Then click on Output range and select any empty cell

See the following box

Then click on OK

So we get the following output

c) From the above output

degrees of freedom = 6 ( n - 1 = 7 - 1 = 6)

From alternative hypothesis this is one tailed test.

So critical value = 1.94318

t test statistic value = 2.065591

d) Here critical t < test t statistic , so we reject the null hypothesis.

Conclusion: At 5% level of significance we have sufficient evidence from to say that the deprivation has a significant effect on hearing threshold.