An insurance company employs agents on a commission basis. It claims that in their first-year agents will earn a mean commission of at least $40,000 and that the population standard deviation is no more than$6,000. A random sample of nine agents found for commission in the first year,

$$\sum_{i=1}^9 x_i=333 \text { and } \sum_{i=1}^9\left(x_i-\bar{x}\right)^2=312$$

where $x_i$ is measured in thousands of dollars and the population distribution can be assumed to be normal. Test, at the $5 level, the null hypothesis that the population mean is at least$40,000.

The owner of Bun ‘N’ Run Hamburgers wishes to compare the sales per day at two locations. The mean number sold for 10 randomly selected days at the Northside site was 83.55, and the standard deviation was 10.50. For a random sample of 12 days at the Southside location, the mean number sold was 78.80 and the standard deviation was 14.25. At the .05 significance level, is there a difference in the mean number of hamburgers sold at the two locations? What is the p-value?

A statement about the value of a population parameter that always includes the equal sign is called the _____.

Are the following statements correct? Which one is better?

$$a).$$

if (age < 16) 
 System.out.println
 (“Cannot get a driver’s license"); 
if (age >= 16) 
 System.out.println
 (“Can get a driver’s license"); 

$$b).$$

if (age < 16)
 System.out.println
 (“Cannot get a driver’s license"); 
else
 System.out.println(“Can get a driver’s license"); 

Opportunity costs are not usually recorded in the accounts of a business. true or false?

A value calculated from sample information used to determine whether to reject the null hypothesis is called the _____.

In a two-tailed test, the rejection region is _____. (all in the upper tail, all in the lower tail, split evenly between the two tails, none of these—pick one)

When conducting a test of hypothesis about a single population mean, the z distribution is used as the test statistic only when the _____ is known.

In a two-sample test of hypothesis for means, the population standard deviations are not known and we must assume what about the shape of the populations?

If the P-value in a statistical test is greater than the level of significance for the test, do we reject or fail to reject $H_{0}$?

Two narrow slits are 0.12 mm apart. Light of wavelength 550 nm illuminates the slits, causing an interference pattern on a screen 1.0 m away. Light from each slit travels to the m = 1 maximum on the right side of the central maximum. How much farther did the light from the left slit travel than the light from the right slit?

A 20.0-mL sample of 0.150 M KOH is titrated with 0.125 M

$$HClO_4$$

solution. Calculate the pH after the following volumes of acid have been added: 20.0 mL.

State whether each of the following is true or false.

a. The significance level of a test is the probability that the null hypothesis is false.

b. A Type I error occurs when a true null hypothesis is rejected.

c. A null hypothesis is rejected at the 0.025 level but is not rejected at the 0.01 level. This means that the p-value of the test is between 0.01 and 0.025.

d. The power of a test is the probability of accepting a null hypothesis that is true.

e. If a null hypothesis is rejected against an alternative at the 5% level, then using the same data, it must be rejected against that alternative at the 1% level.

f. If a null hypothesis is rejected against an alternative at the 1% level, then using the same data, it must be rejected against the alternative at the 5% level.

g. The p-value of a test is the probability that the null hypothesis is true.

Music streaming services are the most popular way to listen to music. Data gathered over the last 12 months show Apple Music was used by an average of 1.65 million households with a sample standard deviation of 0.56 million family units. Over the same 12 months Spotify was used by an average of 2.2 million families with a sample standard deviation of 0.30 million. Assume the population standard deviations are not the same. Using a significance level of .05, test the hypothesis of no difference in the mean number of households picking either service.