Question

A researcher wishes to study whether classical music has any effect on the ability to memorize information.

A random sample of 57 adults were given a memory test in a quiet room. Then they were given a second
memory test while listening to classical music. On the second test, 39 people received a higher score, 15
received a lower score, and 3 received the same score. A sign test at the 0.10 significance level will be
used to test the claim that the music has no effect on memorization ability.
Round your answers to 3 places after the decimal point, if necessary.
(a) What is the value of the test statistic used in this sign test?
Test statistic's value:
(b) Give the value(s) of the critical value(s) used in this sign test. If there are two critical values, enter
them both with a comma between them.
Critical value(s):

Answer 1

The value of the test statistic used in this sign test is 3.178.

The critical value(s) used in this sign test at the 0.10 significance level is ±1.645.

Step-by-step explanation:

To conduct a sign test, we count the number of individuals whose second test score is higher than the first test score.

In this case, 39 individuals received a higher score, 15 received a lower score, and 3 received the same score.

The test statistic is calculated using the formula: Test statistic = absolute value of (number of individuals with higher scores - number of individuals with lower scores) / square root of (number of individuals with higher scores + number of individuals with lower scores + number of individuals with the same scores)

Plugging in the values from the study:

Test statistic = |39 - 15| / sqrt(39 + 15 + 3)

= 24 / sqrt(57)

= 3.178

The critical value(s) for a sign test can be found in a sign test table.

At the 0.10 significance level, with a two-tailed test, the critical value is ±1.645.