Based on the given information, the p-value = 0.0075. Option 2
How to calculate the p-value for this hypothesis test
To calculate the p-value for this hypothesis test, perform a one-sample t-test using the given sample data.
Given:
Sample size (n) = 21
Sample mean (x) = 4.817 weeks
Sample standard deviation (s) = 1.26 weeks
Mean adoption time for animals (μ) = 4 weeks
Significance level (α) = 0.01 (1%)
First, calculate the test statistic (t-score) using the formula:
t = (x - μ) / (s /
(n))
Substituting the values:
t = (4.817 - 4) / (1.26 /
(21))
Calculating this expression:
t ≈ 2.401
Next, find the p-value associated with this test statistic. The p-value represents the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true.
To find the p-value, use statistical software or the t-distribution table.
For a one-tailed test with a significance level of 0.01 and degrees of freedom (df) = n - 1 = 21 - 1 = 20, we find that the p-value is approximately 0.0075.
Therefore, the correct answer is:
The p-value = 0.0075.
You may need to use the appropriate technology to answer this question.
Alonte volunteers at a local animal shelter that works to keep the mean adoption time for animals to be at most four weeks. Alonte's friend Zana conducts a random sample of 21
animals from the shelter and finds the mean time for them to have been adopted was 4.817 weeks with a standard deviation of 1.26 weeks. Zana wants to determine if this provides evidence at the
1% level of significance of a longer mean time than wanted for the shelter. Calculate the p-value.
The p-value =0.0038.
The p-value =0.0075.
The p-value =0.4123.
The p-value =0.9962.