Answer :
The type of error that could have occurred is a Type I error (alpha), and the chances of that happening are 10% in this case
To test if the true average temperature of covid patients exceeds 100, we can use a one-sample t-test.
Given that we have a random sample of 31 covid patients with an average temperature of 101.2 and a known population standard deviation of 3, we can calculate the test statistic and compare it to the critical value at a 10% alpha level.
The test statistic is calculated using the formula:
t = (sample mean - hypothesized population mean) / (population standard deviation/[tex]\sqrt{(sample size)}[/tex])
In this case, the hypothesized population mean is 100, the sample mean is 101.2, the population standard deviation is 3, and the sample size is 31.
Plugging in these values, we get:
t = (101.2 - 100) / (3 / [tex]\sqrt{(31)}[/tex])
t = 1.2 / (3 / 5.57)
t ≈ 1.2 / 0.537
t ≈ 2.23
To determine if this test statistic is significant at the 10% alpha level, we need to compare it to the critical value. Since the alternative hypothesis is that the true average temperature exceeds 100, this is a one-tailed test.
Looking up the critical value in a t-table with 30 degrees of freedom and a 10% significance level, we find that the critical value is approximately 1.697.
Since the test statistic (2.23) is greater than the critical value (1.697), we reject the null hypothesis and conclude that there is evidence to suggest that the true average temperature of covid patients exceeds 100.
Now let's discuss the type of error that could have occurred and the chances of that happening.
In hypothesis testing, there are two types of errors:
1. Type I error (alpha): This occurs when we reject the null hypothesis when it is actually true. In this context, it would mean concluding that the true average temperature exceeds 100 when it actually does not. The chances of committing a Type I error are equal to the significance level, which is 10% in this case.
2. Type II error (beta): This occurs when we fail to reject the null hypothesis when it is actually false. In this context, it would mean failing to conclude that the true average temperature exceeds 100 when it actually does. The chances of committing a Type II error depend on the effect size, sample size, and the chosen significance level. Without additional information, we cannot determine the exact chances of committing a Type II error.
So, in summary, the type of error that could have occurred is a Type I error (alpha), and the chances of that happening are 10% in this case.
Learn more about Type I error here:
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