Question

In a clinic, the systolic blood pressures in mmHg of a random sample of 10 patients with a certain metabolic disorder were collected. Assume blood pressure is normally-distributed in the population. The mean of this sample was 103.2 mmHg with a (sample) standard deviation of 15.0 mmHg. Test the hypothesis that the mean blood pressure of this sample of patients differs from the known population mean sysolic blood pressure of 121.2 mmHg.

Show your working including null hypothesis, alternative hypothesis, test statistic and p-value, and interpret your p-value. Also give a 95% confidence interval. What experimental design is this? What do we mean by “a random sample” in the question?

If the population standard deviation was actually known to be 15.0 mmHg exactly (from previous large studies), compute your p-value in this case.

Answer 1

(a)

Question:

Show your working including null hypothesis, alternative hypothesis, test statistic and p-value, and interpret your p-value.

(i)

H0: Null Hypothesis: = 121.2 ( The mean blood pressure of this sample of patients does not differ from the known population mean sysolic blood pressure of 121.2 mmHg.)

(ii)

HA: Alternative Hypothesis: 121.2 ( The mean blood pressure of this sample of patients differs from the known population mean sysolic blood pressure of 121.2 mmHg.) (Claim)

(iii)

= 103.2

s = 15.0

n = 10

= 0.05

df = 10 - 1 =9

From Table, critical values of t = 2.262

Test Statistic is given by:

(iv)

By Technology,

p -value = 0.0043

(v)

Since p - value = 0.0043 is less than = 0.05, the difference is sigificant. Reject null hypothesis.

Conclusion:
The data support the claim that the mean blood pressure of this sample of patients differs from the known population mean sysolic blood pressure of 121.2 mmHg.

(b)

Question:

Also give a 95% confidence interval.

= 103.2

s = 15.0

n = 10

= 0.05

df = 10 - 1 =9

From Table, critical values of t = 2.262

Confidence Interval:

So,

Answer is:

(92.47, 113.93)

(c)

Question:

What experimental design is this?

This is descriptive research,

because in this experimentation, the researcher seeks to describe the current status of a variable, here: blood pressure of patients

(d)

Question:

What do we mean by “a random sample” in the question?

In the question, a random sample means each item in the sample has the same probablity of selection: Simple Random Sampling (SRS)

(e)

Question:

If the population standard deviation was actually known to be 15.0 mmHg exactly (from previous large studies), compute your p-value in this case.

(i)

H0: Null Hypothesis: = 121.2 ( The mean blood pressure of this sample of patients does not differ from the known population mean sysolic blood pressure of 121.2 mmHg.)

(ii)

HA: Alternative Hypothesis: 121.2 ( The mean blood pressure of this sample of patients differs from the known population mean sysolic blood pressure of 121.2 mmHg.) (Claim)

(iii)

= 103.2

= 15.0

n = 10

= 0.05

From Table, critical values of Z = 1.96

Test Statistic is given by:

(iv)

By Technology,

p -value = 0.0001

(v)

Since p - value = 0.0001 is less than = 0.05, the difference is sigificant. Reject null hypothesis.

Conclusion:
The data support the claim that the mean blood pressure of this sample of patients differs from the known population mean sysolic blood pressure of 121.2 mmHg.