Episodes of dehydration are common at outdoors music festivals. At a particular large annual event, a first
aid team has recorded over the years 85 cases on average per day. In 2018, during a weekend they observe 78, 86,
79, and 81 cases. Assuming the distributions of cases is normal, can you confirm that the number of cases has
significantly dropped in 2018? Assume alpha=0.10
I'm confused as to what would n (the sample size) be? would it be 85?
n = 4, the values are 78, 86, 79, and 81. Compare to mean = 85.
To determine if the number of cases has significantly dropped in 2018, we can perform a hypothesis test. Here's how you can approach it:
Step 1: State the null and alternative hypotheses:
- Null Hypothesis (H0): The average number of cases in 2018 is equal to the average number of cases recorded over the years (μ = 85).
- Alternative Hypothesis (HA): The average number of cases in 2018 is less than the average number of cases recorded over the years (μ < 85).
Step 2: Choose a significance level (alpha):
- The significance level (alpha) is given as 0.10 in this case.
Step 3: Calculate the test statistic:
- Since we know the population standard deviation is not known, we'll use the t-test. The formula for the t-test statistic is:
t = (x̄ - μ) / (s / √n)
where x̄ is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.
Step 4: Determine the critical value:
- The critical value is the value beyond which we reject the null hypothesis. In this case, since we are testing if the number of cases has dropped, we'll use a left-tailed test.
- With a significance level of 0.10 and our degrees of freedom (df) equal to n - 1, we can find the critical value using a t-table or a t-distribution calculator.
Step 5: Compare the test statistic with the critical value:
- If the test statistic is less than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Step 6: Interpret the result:
- If we reject the null hypothesis, it means there is sufficient evidence to conclude that the number of cases has significantly dropped in 2018. If we fail to reject the null hypothesis, we do not have enough evidence to claim a significant drop in the number of cases.
By following these steps and performing the necessary calculations, you should be able to determine if the number of cases has significantly dropped in 2018.