Question

A sample of 10 mothers wants to know if they sleep less than the population in terms of the number of hours they sleep. Their average number of hours they sleep is 6.8. We know that the average hours of sleep in the population is 8 with a standard deviation of 3.

Conduct a z test to see if the sample of mothers differs from the population.

(Be sure to complete all four steps of a hypothesis test.) α=.05

Ackerman and Goldsmith (2011) report that students who study from a screen (phone, tablet, or computer) tended to have lower quiz scores than students who studied the same material from printed pages. To test this finding, a professor identifies a sample n=16 of students who used the electronic version of the course textbook and determines that this sample had an average score of M=72.5 on the final exam. During the previous three years, the final exam scores for the general population of students taking the course averaged μ=77 with a standard deviation of σ=8 and formed a roughly normal distribution. The professor would like to use the sample to determine whether students studying from an electronic screen had exam scores that are significantly different from those for the general population.

1. Assuming a two-tailed test, state the null hypothesis in a sentence that includes the two variables being examined.

2. Using the standard four-step procedure, conduct a two-tailed hypothesis test with α=.05  to evaluate the effect of studying from an electronic screen

Answer 1

Here claim is that the sample of mothers differs from the population.

So hypothesis is vs

As population standard deviation is known, we can convert x to z

As it is two tailed test, P value is

As P value is greater than alpha, we fail to reject the null hypothesis, hence we do not have sufficient evidence to support the claim that the sample of mothers differs from the population