Answer:
Ha: μ < 24
The test statistic is z = -1.75.
The pvalue of the test is 0.0401 > 0.02, which means that we do not reject the null hypothesis, as there is insufficient evidence.
Step-by-step explanation:
A recent survey reported that small businesses spend 24 hours a week marketing their business.
This means that the null hypothesis is:
A local chamber of commerce claims that small businesses in their area are not growing because these businesses are spending less than 24 hours a week on marketing.
This means that the alternate hypothesis is:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis, is the standard deviation and n is the size of the sample.
24 is tested at the null hypothesis:
This means that
The chamber conducts a survey of 93 small businesses within their state and finds that the average amount of time spent on marketing is 23.0 hours a week.
This means that
The population standard deviation is 5.5 hours
This means that
Value of the test-statistic:
The test statistic is z = -1.75.
Do we reject the null hypothesis? Is there sufficient or insufficient evidence?
The pvalue of the test is the probability of finding a sample mean below 23, which is the pvalue of z = -1.75.
Looking at the z table, z = -1.75 has a pvalue of 0.0401
The pvalue of the test is 0.0401 > 0.02, which means that we do not reject the null hypothesis, as there is insufficient evidence.