Explore Samples with Step-by-Step Examples and Expert Guidance

1. A sample is chosen randomly from a population model that was strongly skewed to the right with m =145 and s =100 .
a. If we draw a random sample of n = 1000 from this population, what will be the shape of the histogram based this sample? What would be your best guess of mean and standard deviation of this sample?
b. If we draw 10,000 samples of size n = 1000 from this population, what will be the shape of the histogram of the sample means. What would be your best guess of sample mean and sample standard deviation of the distribution represented by this histogram?

Why is a sample statistic a random variable?

For a continuous random variable x, the population mean and standard deviation are 120 and 15 respectively. How do you find the mean and standard deviation of the sampling distribution of the sample mean for a sample of 25 elements?

What is the mean of the sampling distribution of the sample mean x if a sample of 64 students is selected at random from the entire freshman class?

Suppose that the sample mean for a random sample of 110 cars is 28.3 miles and assume the standard deviation is 3.2 miles. Is 26.9 against the alternative hypothesis that it is not 26.9? What is the test statistic?

If the sample mean = 16, population mean = 8, sample standard deviation = 4, and sample size = 150, what is the one sided t-score of the sample?

A sample of 50 values has a mean of 8.33 while the population standard deviation is 0.67. According to the Central Limit Theorem, the distribution of sample means is what?

As sample size increases, what happens to the standard error of M?

Do all pure samples of a given compound have the same percent composition?

How do you calculate the sample range, sample mean, sample median, sample variance, and sample standard deviation of 18, 19, 34, 38, 24, 18, 22, 51, 44, 14, 29?

You are the assistant manager at Extra Credit Union. Your boss, Robin Banks, has sent you the following email:
"Assistant Manager, as you know, we go the extra mile in our service to our clients. Part of that is knowing our clients well. Thus, we are wanting to solicit phone-call feedback from some of our clients. I know we don't have time to talk to all 10,000 clients, so I am wanting a smaller representative sample. Perhaps a random sample of 25 or 50 would be good. Across all 10,000 clients, the average account balance is $12,000 and the standard deviation is $5000. I want the sample we take to closely match our clients as a whole. Specifically, I want the probability to be at least 80% that the average of our sample is within $1000 of the average for all clients. Would a random sample of 25 be fine or do we need to take a random sample of 50? Use the magical statistics skills you learned back in college and get back to me ASAP! Thanks, Robin Banks"
In your response indicate whether 25 is sufficient or whether a sample of 50 would be necessary. (You will want to calculate the probability of the sample mean being between $11,000 and $13,000 for both a sample size of 25 and 50.)

How many different phone numbers are possible in the area code 928? Note: Phone numbers cannot start with 0 or 1.

At a football game, a researcher randomly asks 100 people to name their favorite sport. Is this a biased sample?

When should blood samples for trough drug levels be collected?

What is the mode of the following numbers? $12,11,14,10,8,13,11,9$
$$\begin{gathered} a11 \\ b.10 \\ c.14 \\ d.8 \end{gathered}$$

In what way are voluntary response samples often biased?

Why is sampling necessary?

Why do statisticians use samples?

A chemist weighed three separate test samples at 0.17 gram, 0.204 gram, and 2.3 grams. What is the total weight of the three samples?

The mass of Denise's rock sample is 684 grams. The mass of Pauline's rock sample is 29,510 centigrams. How much greater is Denise's sample than Pauline's sample?