Question

You think that your class might be happier than the general population. You want to conduct a hypothesis test to see if you are right. Thus, you randomly sample 9 students in your class and find that they have a mean happiness score of 3.25, with a standard deviation of 1. You know information about the population distribution. First, you know the population scores are normally distributed. You also know that the mean happiness score for the population from which these 9 students were drawn is 3.5 and the standard deviation is 1.2.

a. Identify the name of the test you will employ to see if your class is happier than the general population. (4 points)

b. Conduct a formal null hypothesis significance test, making sure to include every step and to fully write out your answers, making sure to state the hypothesis in words and using symbolic notation. (for your test statistic, write out your equation and calculate the final answer.)  (11 points). If you need specific symbols, we have put some here for you to copy and paste into your text entry box answer: > < ≥ ≤ = ≠ ± + - x Σ x̄ x̂ ȳ ŷ y’ μ H₀ H₁

Answer 1

Answer:

(a) The test used will be the one-sample z-test,

(b) The hypothesis being tested is:

H0: µ 3.5

Ha: µ 3.5

x = 3.25

n = 9

σ = 1.2

The test statistic, z = (x - µ)/σ/√n

z = (3.25 - 3.5)/1.2/√9

z = -0.63

The p-value is 0.7340.

Since the p-value (0.7340) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that the class is happier than the general population.

Please give me a thumbs-up if this helps you out. Thank you!