Population Standard Deviation Made Easy: Learn with Examples, Equations, and Expert Tips

Choose the correct answer:
We use the t distribution to perform a hypothesis test about the population mean when:
a. The population from which the sample is drawn is approximately normal and the population standard deviation is known
b. The population from which the sample is drawn is not approximately normal and the population standard deviation is known.
c. The population from which the sample is drawn is approximately normal or sample size is 30 or larger and the population standard deviation is unknown.
d. The population from which the sample is drawn is not approximately normal and the population standard deviation is unknown.

For a sample of n = 16 scores, what is the value of the population standard deviation $(\mathrm{\sigma <!--\; \sigma \; -->})$ necessary to produce each of the following a standard error values?
${\mathrm{\sigma <!--\; \sigma \; -->}}_M$ = 8 points?

Which of the following statements is true about the t-distribution?
a) For large sample sizes, the t-distribution has the same properties as the normal curve.
b) For small sample sizes, the t-distribution has the same properties as the normal curve.
c) Like the Normal distribution, the t-distribution is symmetric for small n.
d) Since population standard deviation is usually unknown, the standard error uses the sample standard deviation to estimate population standard deviation.

When conducting a hypothesis test for the population mean, you will not know the population standard deviation, so you will have to use the sample standard deviation instead. How will this affect the process?

A sample is selected from a population with a mean of $\mathrm{\mu <!--\; \mu \; -->}=40$. If the sample mean is $M=45$, which of the following combinations would make the sample mean a good, representative value for the population?​
Question options:
a. ​A small sample and a large population standard deviation
b. ​A large sample and a large population standard deviation
c. ​A small sample and a small population standard deviation
d. ​A large sample and a small population standard deviation

Suppose that you are constructing a survey of average student loan debt. You decide that instead of sampling 50 students, you are going to sample 75 students. When you do this, the
a. standard error of the mean decreases O
b. population mean increases O
c. standard deviation of the population decreases
d. standard error of the mean increases

Degress of freedom are used to correct for the fact that population standard deviation will always be less precise than the sample standard deviation. True or False?

Assuming that these wages constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places.
16, 35, 13, 25, 36

A public safety association suspects that long distance truck drivers are getting behind the wheel with too little sleep. A sample of 50 drivers yields a sample average of 6 hours of sleep every night with a sample standard deviation 2 hours. Which of the following statements is true ?
a. The sample standard deviation, 2 hours, is a point estimate of the population standard deviation
b. The sample mean, 6 hours, is a point estimate of the population standard deviation.
c. The sample standard deviation, 2 hours, is a point estimate of the population mean
d. The sample mean, 6 hours, is a point estimate of the population mean

We want to conduct a hypothesis test of the claim that the population mean score on a nationwide examination in anthropology is different from 492. So, we choose a random sample of exam scores. The sample has a mean of 505 and a standard deviation of 75. For each of the following sampling scenarios, choose an appropriate test statistic for our hypothesis test on the population mean. Then calculate that statistic. Round your answers to two decimal places. The sample has size 12, and it is from a normally distributed population with an unknown standard deviation. Oz = = 0 O It is unclear which test statistic to use.

Consider the following.
22, 11, 33, 24, 21
Compute the population standard deviation of the numbers.

A score that is 9 points above the mean corresponds to a z score of +1. What is the population standard deviation?

True or False? The population standard deviation and sample standard deviation are of the same value if the population and sample size are the same.

A population of 33 scores has a sum of squared deviations value of SS = 507.09. What would be the population's standard deviation? Be sure to submit a numeric response that is rounded to the nearest hundredth.

We have provided simple data sets for you to practice the basics of finding a population standard deviation.
1, 2, 4, 4

Suppose the standard deviation of the sample mean is equal to 0.6. If a sample of size n=100n=100 is collected, what is the population standard deviation?

In the following situations, indicate whether you’d use the normal distribution, the t distribution, or neither.
a. The population is normally distributed, and you know the population standard deviation.
b. You don’t know the population standard deviation, and the sample size is 35.
c. The sample size is 22, and the population is normally distributed.
d. The sample size is 12, and the population is not normally distributed.
e. The sample size is 45, and you know the population standard deviation.

Suppose X∼Bin(12,0.65). Find the population standard deviation.

A sample standard deviation for the number of passengers taking a particular airline flight is 8. A 95% confidence interval estimate of the population standard deviation is 5.86 passengers to 12.62 passengers. Was a sample size of 10 or 15 used in the statistical analysis?

A variable of a population has a normal distribution. Suppose that you want to find a confidence interval for the population mean.
a. If you know the population standard deviation, which procedure would you use?
b. If you do not know the population standard deviation, which procedure would you use?