Question

question 21 score on last try: 0 of 2 pts. see details for more. at least one scored part is incorrect. jump to first changeable incorrect part. > next question get a similar question you can retry this question below the effectiveness of a blood - pressure drug is being investigated. an experimenter finds that, on average, the reduction in systolic blood pressure is 32.3 for a sample of size 22 and standard deviation 13.5. estimate how much the drug will lower a typical patients systolic blood pressure (using a 99% confidence level). assume the data is from a normally distributed population. enter your answer as a tri - linear inequality accurate to three decimal places. 24.154 < μ < 40.440

Explanation:

Step1: Identify the formula for confidence - interval

For a small sample ($n<30$) and unknown population standard - deviation, the formula for a confidence interval of the population mean $\mu$ is $\bar{x}-t_{\alpha/2}\frac{s}{\sqrt{n}}<\mu<\bar{x} + t_{\alpha/2}\frac{s}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $s$ is the sample standard deviation, $n$ is the sample size, and $t_{\alpha/2}$ is the critical value.

Step2: Determine the degrees of freedom and $\alpha$

The degrees of freedom $df=n - 1=22-1 = 21$. The confidence level is $99\%$, so $\alpha=1 - 0.99 = 0.01$ and $\alpha/2=0.005$.

Step3: Find the critical value $t_{\alpha/2}$

Looking up in the $t$-distribution table or using a calculator, for $df = 21$ and $\alpha/2=0.005$, $t_{0.005,21}= 2.831$.

Step4: Calculate the margin of error $E$

The sample mean $\bar{x}=32.3$, the sample standard deviation $s = 13.5$, and the sample size $n = 22$. The margin of error $E=t_{\alpha/2}\frac{s}{\sqrt{n}}=2.831\times\frac{13.5}{\sqrt{22}}\approx2.831\times\frac{13.5}{4.69}=2.831\times2.88 = 8.154$.

Step5: Calculate the confidence interval

The lower limit is $\bar{x}-E=32.3 - 8.154=24.146$. The upper limit is $\bar{x}+E=32.3 + 8.154=40.454$.

Answer:

$24.146<\mu<40.454$