A recent survey reported that small businesses spend 24 hours a week marketing their business. 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. The chamber conducts a survey of 88 small businesses within their state and finds that the average amount of time spent on marketing is 23.2 hours a week. Assuming that the population standard deviation is 4.2 hours, is there sufficient evidence to support the chamber of commerce’s claim at the 0.05 level of significance?
Step 1 of 3:
State the null and alternative hypotheses for the test. Fill in the blank below. H0Ha: μ=24: μ⎯⎯⎯⎯⎯⎯⎯⎯24
Step 2 of 3: Compute the value of the test statistic. Round your answer to two decimal places.
Step 3 of 3: Draw a conclusion and interpret the decision.

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codiepienagoya codiepienagoya · Answer 1 · 2021-04-27T09:40:25+02:00

Answer:

Following are the responses to the given choices:

Step-by-step explanation:

In step 1:

State the zero and alternate test hypotheses. Insert underneath.

[tex]H_0 : \mu = 24: H_a : \mu < 24[/tex]

[tex]H_0[/tex] Smaller companies in their region are and they spend at least 24 hours per week on the marketing of the these companies

[tex]H_1[/tex] There really is no growth for smaller firms in their area because the companies spend or less 24 hours per week on marketing.

In step 2:

Each test statistics meaning is calculated. Around two decimal places for your reply.

[tex]z=\frac{\bar{X}-\mu_{0}}{\frac{\sigma}{\sqrt{n}}}=\frac{23.2-24}{\frac{4.2}{\sqrt{88}}}=-1.787[/tex]

In step 3:

Draw a start and write the decision.

Since it is observed that [tex]z=-1.787 < z_c=-1.64[/tex] it is then concluded that the null hypothesis is rejected.

Consequently we consider that small companies in their field may not expand, as they spend or less 24 hours per week on marketing.