Hypothesis test with one-mean z-test
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Scenario: Delta Apple Pi claims that their brothers get on average 25 Tinder matches per day. However, word is that it's actually higher than that, so you collect a random sample of 35 Delta Apple Pi brothers' daily Tinder matches. You measure a mean of 26.5 daily matches. It is known that the population standard deviation is 5.7 matches. Provide support for your claim using a hypothesis test with an alpha level of 0.05.
| Clue | Insight |
|---|---|
| We measured a mean of 26.5 in our sample. | We're working with means here. |
| We're given the population standard deviation of 5.7, and our sample of 35 is greater than 30. | We can use a z-test here (instead of a t-test). |
| The scenario ends with "hypothesis test". | We're conducting a hypothesis test here. |
| Assumption | Validate |
|---|---|
| Sample is randomly selected from the population. | We can see "random sample" in the scenario. ✅ |
| The sample size (n) is less than or equal to 10% of the population size (N). | We can assume our sample of 35 brothers is less than 10% of the entire Delta Apple Pi chapter. ✅ |
| The sample size is greater than or equal to 30, or the population itself is normally distributed. | Our sample of 35 is greater than 30! ✅ |
H0: µ = 25
Ha: µ > 25
We're conducting a z-test, so our test statistic will be a z-score with sample means!
x-bar is the sample mean we observed.
µ0 is the population mean claimed by the null hypothesis (H0).
σ is the population standard deviation.
n is the sample size.
x-bar = 26.5
µ0 = 25
σ = 5.7
n = 35
z = (26.5 - 25) / (5.7 / √[35])
z = (1.5) / (5.7 / 5.916)
z = (1.5) / (0.963)
z = 1.56
p-value = 0.9406
But wait a second...
We're working with a one-tail test, specifically the right-tail of the distribution, since our alternative hypothesis uses >!
p-value = 0.0594
α = 0.05
Considering our p-value of 0.0594 is greater than our alpha level of 0.05, this means we'll fail to reject the null hypothesis!
Answer: Since our p-value of 0.0594 is greater than our alpha level of 0.05, we fail to reject the null hypothesis and do not have enough evidence to support the alternative hypothesis, which states the brothers of Delta Apple Pi have an mean daily Tinder match value greater than 25.