Question

It is known that a particular laboratory task takes the average person 2.5 seconds. A researcher was interested in whether older people are slower (take longer) on this task. The researcher tested 30 randomly selected 80-year-olds. Their mean time was 2.7 seconds, with an estimated population standard deviation of 1.4 seconds. What should the researcher conclude (use the .05 level)?
a. /2 Identify the populations involved

Answer 1

Given :

n = 30

x' = 2.7

σ = 1,4

∝ = 0.05

To find :

What should the researcher conclude (use the .05 level)?

Solution :

Step 1

The hypothesis is given by

H₀:μ = 2.5

H₁:μ ≠ 2.5

Step 2

Level of significance ∝ = 0.05

Step 3

Test statistic Z = (x'-μ)(σ / √n)

Z = (2.7 - 2.5)(1.4 / √30)

Z = 0.78

Step 4

Decision

p-value = 0.4343

p-value > ∝ → Fail to reject H₀

Step 5

Conclusion

There is insufficient evidence to conclude this test