Question

Think about a population mean that you may be interested in and propose a hypothesis test problem for this parameter. Gather appropriate data and post your problem. Include the null and alternative hypothesis, alpha value, p-value, and a conclusion. Make sure that you use appropriate terminology, specify whether you are using the classical method or the p-value method, and fully explain your solution.

How do we determine that we are to fail to reject the null hypothesis? What process do we use to determine this result?

A principle is curious about how many hours per week students’ study in the grade 10 psychology class. It is believed for each student to be successful in the class, they must spend at least 6 hours/week studying. He went on to ask 7 random students to keep track of the amount of time each week they study and it was concluded that the average was 6.5 hrs.

Results: 6.5 9 7 7 8 5 3

Standard deviation: 2 hours

H0: μ = 6 hrs HA: μ > 6 hrs

α = 0.05 significance level

N= 7 X= 6.5

Answer 1

To test $H_0:\mu = 6$ against $H_a:\mu > 6$

Here

sample mean $\bar{x} = 6.5$

population standard deviation $\sigma = 2$

and sample size

The test statistic can be written as

$z = \frac{\sqrt{n}(\bar{x} - 6)}{\sigma }$ which under H₀ follows a standard normal distribution.

We reject H₀ at 5% level of significance if p-value < 0.05

Now,

The value of the test statistic

and p-value =

Since p-value > 0.05, so we fail to reject H₀ at 5% level of significance and we can conclude that the mean amount of time is not significantly greater than 6.5