Question

Suppose the mean blood pressure for people in a certain country is 130 mmHg with a standard deviation of 23 mmHg. Blood pressure is normally distributed.

State the random variable.

• The blood pressure of a person in the country.
• The mean blood pressure of people in the country.
• The standard deviation of blood pressures of people in the country.

Suppose a sample of size 14 is taken. State the shape of the distribution of the sample mean.

• The shape of the sampling distribution of the sample mean is unknown since the population of the random variable is normally distributed and the sample size is less than 30.
• The sampling distribution of the sample mean is normally distributed since the population is normally distributed.
• The sampling distribution of the sample mean is unknown since the sample size is less than 30.

Suppose a sample of size 14 is taken. State the mean of the sample mean.
μ_x̄ =

Suppose a sample of size 14 is taken. State the standard deviation of the sample mean. Round to two decimal places.
σ_x̄ =

Suppose a sample of size 14 is taken. Find the probability that the sample mean blood pressure is more than 133 mmHg. Round to four decimal places.
P(x̄ > 133) =

Would it be unusual to find a sample mean of 14 people in the country of more than 133 mmHg? Why or why not?

• It would not be unusual for the sample mean of 14 people in the country to be more than 133 since the probability is less than 0.05.
• It would be unusual for the sample mean of 14 people in the country to be more than 133 since the probability is less than 0.05.
• It would be unusual for the sample mean of 14 people in the country to be more than 133 since the probability is at least 0.05.
• It would not be unusual for the sample mean of 14 people in the country to be more than 133 since the probability is at least 0.05.

If you did find a sample mean for 14 people in the country to be more than 133 mmHg, what might you conclude?

• Since it is not unusual for the sample mean of 14 people in the country to be more than 133, there is no evidence that the population mean has changed.
• Since it is not unusual for the sample mean of 14 people in the country to be more than 133, it may indicate that the population mean has changed.
• Since it is unusual for the sample mean of 14 people in the country to be more than 133, there is no evidence that the population mean has changed.
• Since it is unusual for the sample mean of 14 people in the country to be more than 133, it may indicate that the population mean has changed.

Answer 1

Suppose the mean blood pressure for people in a certain country is 130 mmHg with a standard deviation of 23 mmHg. Blood pressure is normally distributed.

State the random variable.

X : The blood pressure of a person in the country.

Suppose a sample of size 14 is taken. State the shape of the distribution of the sample mean.

• The shape of the sampling distribution of the sample mean is unknown since the population of the random variable is normally distributed and the sample size is less than 30.

Suppose a sample of size 14 is taken. State the mean of the sample mean.
μ_x̄ = 130

Suppose a sample of size 14 is taken. State the standard deviation of the sample mean. Round to two decimal places.
σ_x̄ = 23/Sqrt(14) = 6.15

Suppose a sample of size 14 is taken. Find the probability that the sample mean blood pressure is more than 133 mmHg. Round to four decimal places.
P(x̄ > 133) =0.3128

Computing the probability for any small sample size is in general gives the overall idea of the situation. When sample size increases the situation seems to be more stable in terms of probability