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2022-09-25
Answered

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.

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Marley Stone

Answered 2022-09-26
Author has **13** answers

In this hypothesis case, we need to test the claim that population mean score in anthropology is different from 492.

The t-test is used when the data is from normal distribution and the population standard deviation is unknown. In this case, as the population standard deviation is NOT KNOWN, hence we will use T-TEST.

Thus, the correct option is:

$\mu =\text{population mean}=492\phantom{\rule{0ex}{0ex}}\overline{x}=\text{sample mean}=505\phantom{\rule{0ex}{0ex}}s=\text{sample standard deviation}=75\phantom{\rule{0ex}{0ex}}n=\text{sample size}=12$

$t=\frac{\overline{x}-\mu}{s/\sqrt{n}}\phantom{\rule{0ex}{0ex}}=\frac{505-492}{75/\sqrt{12}}\phantom{\rule{0ex}{0ex}}\approx 0.60$

Hence, t=0.60

The t-test is used when the data is from normal distribution and the population standard deviation is unknown. In this case, as the population standard deviation is NOT KNOWN, hence we will use T-TEST.

Thus, the correct option is:

$\mu =\text{population mean}=492\phantom{\rule{0ex}{0ex}}\overline{x}=\text{sample mean}=505\phantom{\rule{0ex}{0ex}}s=\text{sample standard deviation}=75\phantom{\rule{0ex}{0ex}}n=\text{sample size}=12$

$t=\frac{\overline{x}-\mu}{s/\sqrt{n}}\phantom{\rule{0ex}{0ex}}=\frac{505-492}{75/\sqrt{12}}\phantom{\rule{0ex}{0ex}}\approx 0.60$

Hence, t=0.60

asked 2022-07-31

The quality-control inspector of a production plant will reject a batch of syringes if two or more defective syringes are found in a random sample of twelve syringes taken from the batch. Suppose the batch contains 1% defective syringes.

(b)

Find 𝜇 (in terms of the number of syringes). (Enter a number. Enter your answer to two decimal places.)

𝜇 = syringes

What is the expected number of defective syringes the inspector will find? (Enter a number. Enter your answer to two decimal places.)

(c)

What is the probability that the batch will be accepted? (Enter a number. Round your answer to three decimal places.)

(d)

Find 𝜎 (in terms of the number of syringes). (Enter a number. Round your answer to three decimal places.)

𝜎 = syringes

asked 2022-08-30

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.

asked 2022-10-18

A sample is selected from a population with a mean of $\mu =40$. 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

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

asked 2022-09-27

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

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

asked 2022-09-30

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

16, 35, 13, 25, 36

asked 2022-10-12

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?

asked 2022-08-17

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.

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.