Basic Concepts on Hypothesis Testing

Which of the following would be an appropriate null hypothesis?

• The mean of a population is equal to 50.

• The mean of a sample is equal to 50.

• The mean of a population is greater than 50.

• None of the choices

Which of the following would be an appropriate null hypothesis?

• The population proportion is less than 0.45.

• The sample proportion is less than 0.45.

• The population proportion is no less than 0.45

• The sample proportion is no less than 0.45.

Which of the following would be an appropriate alternative hypothesis?

• The mean of a population is equal o 50.

• The mean of a sample is equal to 50.

• The mean of a sample is greater than 50.

• The mean of a sample is greater than 50.

Which of the following would be an appropriate alternative hypothesis?

• The population proportion is less than 0.45

• The sample proportion is less than 0.45.

• The population proportion is no less than 0.45.

• The sample proportion is no less than 0.45.

A Type II error is committed when

• we reject a null hypothesis that is true

• we don't reject a null hypothesis that is true

• we reject a null hypothesis that is false

• we don't reject a null hypothesis that is false

A Type I error is committed when

• we reject a null hypothesis that is true

• we don't reject a null hypothesis that is true

• we reject a null hypothesis that is false

• we don't reject a null hypothesis that is false

Suppose we wish to test $H_0:\ \mu\le47$   versus  $H_1:\ \mu>47$ . What will be the result if we conclude that the mean is greater than 47 when its true value is really 52?

• We have made a Type I error.

• We have made a Type II error.

• We have made a correct decision.

• None of the choices is correct

If, as a result of a hypothesis test, we reject the null hypothesis when it is false, then we have committed

• a Type II error

• a Type I error

• no error

• an acceptance error

 The owner of a local restaurant has recently surveyed a random sample of $n=250$ customers of the restaurant. She would now like to determine whether or not the mean age of her customers is over 30. If so, she planned to provide background music to appeal to an older crowd. If not, then no changes would be made to the background music in the restaurant. The appropriate hypotheses to test are:

•  $H_0:\ \mu\ \ge30\$  versus  $H_1:\ \mu\ <30$  

•  $H_0:\ \mu\le30$  versus  $H_1:\ \mu\ >30$  

•  $H_0:\ \overline{X}\ge30$  versus  $H_1:\ \overline{X}\ <30$  

•  $H_0:\ \overline{X}\ \le30$  versus  $H_1:\ \overline{X}\ >30$  

A major telco is considering opening a new telecom centre in an area that currently does not have any such renters. The telco will open the centre if there is evidence that more that more than 5,000 of the 20,000 households in the area use the telco. It conducts a poll of 300 randomly selected households in the area and finds that 96 subscribe to the telco. State the test of interest to the rental chain.

• $H_0:\ p\ \le0.32\$ versus $H_1:\ p>0.32$

• $H_0:\ p\ \le0.25\$ versus $\ H_1:\ p>0.25$

• $H_0:\ p\ \le5,000\$ versus $H_1:\ p>5,000$

• $H_0:\ \mu\le5,000\$ versus $H_1:\ \mu>5,000$