Instruction 12 -Referring to Instruction 12

question 10

Short Answer

Instruction 12.29
The managers of a brokerage firm are interested in finding out if the number of new customers a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new customers they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows.
$$\begin{array} { | l | l | l | } \hline \text { Broker } & \text { Clients } & \text { Sales } \\\hline 1 & 27 & 52 \\\hline 2 & 11 & 37 \\\hline 3 & 42 & 64 \\\hline 4 & 33 & 55 \\\hline 5 & 15 & 29 \\\hline 6 & 15 & 34 \\\hline 7 & 25 & 58 \\\hline 8 & 36 & 59 \\\hline 9 & 28 & 44 \\\hline 10 & 30 & 48 \\\hline 11 & 17 & 31 \\\hline 12 & 22 & 38 \\\hline\end{array}$$
-Referring to Instruction 12.29,the managers of the brokerage firm wanted to test the hypothesis that the number of new customers brought in had a positive impact on the amount of sales generated.For a test with a level of significance of 0.01,the null hypothesis should be rejected if the value of the test statistic is____________.

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Definitions:

Sample Variance

A measure of the dispersion or spread of data points in a sample, calculated by taking the average of the squared differences from the mean.

Central Limit Theorem

A statistical theory stating that the distribution of sample means will approximate a normal distribution as the sample size becomes large, regardless of the population's distribution.

Statistical Analyses

The process of collecting, summarizing, and interpreting data to discover patterns and test hypotheses.

T-distribution

A probability distribution that arises when estimating the mean of a normally distributed population in situations where the sample size is small, and the population standard deviation is unknown.