Question

Web business You want to compare the daily sales for two different designs of Web pages for your Internet business. You assign the next $60$days to either Design A or Design B, $30$days to each.

(a) Describe how you would assign the days for Design A and Design B using the partial line of random digits provided below. Then use your plan to select the first three days for using Design A. Show your method clearly on your paper.

$24005521142622439078$

(b) Would you use a one-sided or a two-sided significance test for this problem? Explain your choice. Then set up appropriate hypotheses.

(c) If you plan to use Table B to calculate the P-value, what are the degrees of freedom?

(d) The t statistic for comparing the mean sales is $2.06$Using Table B, what P-value would you report? What would you conclude?

Short answer

(a) $21,24\&55$were selected for design A

(b)$H_0:{\mu }_1={\mu }_2$

$H_a:{\mu }_1\ne {\mu }_2$

(c) The degree of freedom is $29$$29$

(d) The P value is$0.05$

Step-by-step solution

Part (a) Step 1: Given Information

Given in the question that every day of the $60$days a different number between$1and60$. we have to describe how you would assign the days for Design A and Design B using the partial line of random digits provided below. Then use plan to select the first three days for using Design A.

Part (a) Step 2: Explanation

choose the first two-digit number in the $1^{st}$text

If the number falls between $1and60$, choose the day for design A, then disregard the number and move on to the next $2$-digit number. Repeat the process until design A has selected $30$days, with repeated numbers being ignored. The remaining $30$days will be used to construct A.

for the design A, locate the $1^{st}$$3$days

$24\Rightarrow selectday24$

$00\Rightarrow ignore$

$55\Rightarrow selectday55$

$21\Rightarrow selectday21$

therefore,$21,24\&55$ were selected for design A

Part (b) Step 1: Given Information

We have to determine that a one-sided or a two-sided significance test for this problem and Then set up appropriate hypothesis.

Part (b) Step 2: Explanation

If a difference exists, testing is required, and a two-sided significance test is recommended. The null hypothesis states that the population's mean is the same:

$H_0:{\mu }_1={\mu }_2$

The alternative hypothesis states the opposite of the null hypothesis and utilizes the symbol since the two-sided significance test is used.

$H_{\alpha }:{\mu }_1\ne {\mu }_2$

Part (c) Step 1: Given Information

Given in the question that

$n_1=30$

$n_2=30$

we have to determine the degree of freedom.

Part (c) Step 2: Explanation

$$\begin{gathered} df=\min \left(n_1-1,n_2-1\right) \\ =\min (30-1,30-1) \\ =29 \end{gathered}$$

Part (d) Step 1: Given Information

Given in the question that

$n_1=30$

$n_2=30$

$t=2.06$

$H_0:{\mu }_1={\mu }_2$

$H_a:{\mu }_1\ne {\mu }_2$

we have to find out the P value.

Part (d) Step 2: Explanation

The degree of freedom is $29$

The P value is

$$\begin{gathered} 0.04=2\times 0.02<P<2\times 0.025 \\ =0.05 \end{gathered}$$

$P<0.05\Rightarrow reject{H}_0$

There is sufficient evidence to support the notion that there is a difference.