In a population of over 15,000 patients, the distribution of systolic blood pressure follows the normal curve. Investigators believe the average systolic blood pressure in the population is 120 mm. The investigators take a simple random sample of 6 patients from this population. The systolic blood pressure measurements of these patients have an average of 113.5 mm and an SD (computed with 6 in the denominator) of 12.2 mm. Is the average systolic blood pressure in the population lower than the investigators think? Or is this just chance variation?
PROBLEM 9
The null hypothesis is:
The average blood pressure in the population is 120 mm.
The average blood pressure in the population is less than 120 mm.
The average blood pressure in the population is not equal to 120 mm.
PROBLEM 10
The approximate distribution of the test statistic is (pick the best option)
binomial
hypergeometric
normal t
chi-square
PROBLEM 11
The test is
one-tailed
two-tailed
PROBLEM 12
The P-value of the test is approximately _______%
PROBLEM 13
“The test supports what the investigators think.”
The quoted statement is
True
False
9 1
10 4
11 1
13 1
Help, thank you very much
Problem 9:
The null hypothesis in this case is that the average systolic blood pressure in the population is 120 mm.
Problem 10:
The best option for the approximate distribution of the test statistic is a t-distribution. Since the sample size is small (n = 6), we use the t-distribution to perform hypothesis testing.
Problem 11:
The test is one-tailed because we are testing whether the average systolic blood pressure in the population is lower than the investigators think. We are only concerned with the possibility of it being lower, rather than higher or different in general.
Problem 12:
To determine the P-value of the test, we need to calculate the t-statistic. The formula for the t-statistic is:
t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
Plugging in the values from the problem, we have:
t = (113.5 - 120) / (12.2 / sqrt(6))
Once we calculate the t-statistic, we can use a t-table or a statistical software to find the corresponding P-value. Depending on the calculated t-statistic, we will compare it with the critical value(s) from the t-distribution to determine the P-value. The P-value is the probability of obtaining a sample mean as extreme as the one observed, assuming the null hypothesis is true.
Problem 13:
Without knowing the calculated P-value from the previous problem, we cannot determine whether the test supports what the investigators think. We will need to compare the P-value to a predetermined significance level (e.g., 0.05) to decide whether to reject or fail to reject the null hypothesis.