Question

Suppose that memory for unrelated words is distributed normally with a mean of µ = 50 with a standard deviation of σ = 12. A random sample is selected from this population. After a treatment is administered to the individuals in the sample, a memory test that measures memory for unrelated words is administered, the sample mean is found to be M = 55.

If the sample consists of n = 16 scores, can we conclude that the treatment has a significant effect? Use a two-tailed test with α=.05

1.State the null and alternative hypotheses in words and with statistical notation

2.The critical z values are

3.The z-score statistic is:

4.Your decision is

Answer 1

Here that the memory for unrelated words has a mean µ = 50

standard deviation = σ = 12

a random sample is selected from the population after the treatment

Here sample mean M = 55

n = 16

standard error of sample mean = se = σ/sqrt(n) = 12/sqrt(16) = 3

Here we are Using a two-tailed test with α=.05

(1) Here

Null Hypothesis : H₀ : Treatment has no significant effect on memory for unrelated words. µ' = 50

Alternative Hypothesis : H_a : Treatment has significant effect on memory for unrelated words. µ' 50

where µ' is the mean memory for unrelated words after treatment

(2) Here as we are using a two tailed test with alpha = 0.05

Z_critical = +- 1.96

(3) Test statstiic

Z = (M - µ)/se = (55 - 50)/3 = 1.6667

(4) So as we get here that Z < Z_critical so we would fail to reject the null hypothesis and can conclude that Treatment has no significant effect on memory for unrelated words.