Corporate sustainability of CPA firms. Corporate...

Corporate sustainability of CPA firms. Corporate sustainability refers to business practices designed around social and environmental considerations. Refer to the Business and Society (March 2011) study on the sustainability behaviors of CPA corporations, Exercise 2.23 (p. 83). Recall that the level of support for corporate sustainability (measured on a quantitative scale ranging from 0 to 160 points) was obtained for each in a sample of 992 senior managers at CPA firms. Higher point values indicate a higher level of support for sustainability. The accompanying Minitab printout gives a $90 \%$ confidence interval for the mean level of support for all senior manag. ers at CPA firms $$ \begin{aligned} &\text { One-Sample T: Support }\\ &\begin{array}{|c|c|c|c|c|c|c|} \hline \text { Varabin } & & \begin{array}{r} \text { Hean } \\ \text { tht } \end{array} & \text { subev } & \text { 25 Neas } & \begin{array}{r} 900 \\ \cos -390 \end{array} & \text { et } \\ \hline 9-\mathrm{pF} \text { ort } & & 67,759 & 26.472 & & (65-390, & (5,269) \\ \hline \end{array} \end{aligned} $$ a. Locate the $90 \%$ confidence interval on the printout. b. Use the sample mean and standard deviation on the printout to calculate the $90 \%$ confidence interval. Does your result agree with the interval shown on the printout? c. Give a practical interpretation of the $90 \%$ confidence interval. d. Suppose the CEO of a CPA firm claims that the true mean level of support for sustainability is 75 points. Do you believe this claim? Explain.

Corporate sustainability of CPA firms. Corporate sustainability refers to business practices designed around social and environmental considerations. Refer to the Business and Society (March 2011) study on the sustainability behaviors of CPA corporations, Exercise 2.23 (p. 83). Recall that the level of support for corporate sustainability (measured on a quantitative scale ranging from 0 to 160 points) was obtained for each in a sample of 992 senior managers at CPA firms. Higher point values indicate a higher level of support for sustainability. The accompanying Minitab printout gives a $90 \%$ confidence interval for the mean level of support for all senior manag. ers at CPA firms
$$
\begin{aligned}
&\text { One-Sample T: Support }\\
&\begin{array}{|c|c|c|c|c|c|c|}
\hline \text { Varabin } & & \begin{array}{r}
\text { Hean } \\
\text { tht }
\end{array} & \text { subev } & \text { 25 Neas } & \begin{array}{r}
900 \\
\cos -390
\end{array} & \text { et } \\
\hline 9-\mathrm{pF} \text { ort } & & 67,759 & 26.472 & & (65-390, & (5,269) \\
\hline
\end{array}
\end{aligned}
$$
a. Locate the $90 \%$ confidence interval on the printout.
b. Use the sample mean and standard deviation on the printout to calculate the $90 \%$ confidence interval. Does your result agree with the interval shown on the printout?
c. Give a practical interpretation of the $90 \%$ confidence interval.
d. Suppose the CEO of a CPA firm claims that the true mean level of support for sustainability is 75 points. Do you believe this claim? Explain.

Key Concepts

Corporate Sustainability

Corporate sustainability refers to business practices that integrate social and environmental concerns with economic decision-making. This concept emphasizes long-term viability, ensuring that firms not only generate profit but also operate in a way that benefits society and minimizes negative environmental impacts.

Confidence Interval

A confidence interval is a statistical tool used to estimate an unknown population parameter, such as a mean, by providing a range of values that is likely to contain the true parameter. It is calculated from sample data and offers a measure of uncertainty, with the confidence level indicating the probability that the interval contains the parameter.

One-Sample t-Test

The one-sample t-test is a statistical method used to assess whether the mean of a single sample differs significantly from a known or hypothesized population mean. In the context of confidence intervals, the corresponding t-distribution is employed when the sample size is small or when the population standard deviation is unknown, allowing for the construction of an interval estimate for the true mean.

Hypothesis Testing

Hypothesis testing involves making inferences about a population parameter based on sample data. It typically includes comparing an observed statistic (like the sample mean) to a stated value (such as a CEO's claimed mean) to determine if there is sufficient evidence to reject or fail to reject the stated claim. Confidence intervals can be used to support these inferences by showing whether the hypothesized parameter lies within the calculated range.

Transcript

00:01 For this problem, we are told that the level of support for corporate sustainability was obtained for each in a sample of 992 senior managers at cpa firms.

00:12 We have a mini -tab printout here that gives a 90 % confidence level for the mean level of support for all senior managers at cpa firms.

00:20 In part a, we are asked to locate the 90 % confidence interval on the printout.

00:25 So we can see that it is right here, the printout for 60%.

00:31 Or for 90 % ci between 66 .350 and 69 .160.

00:39 Then for part b, we are asked to use the sample mean and standard deviation on the printout to calculate the 90 % confidence interval.

00:47 We are asked, does our result agree with the interval shown on the printout? now to do that, we can see that we have that the sample mean x bar equals 67 .755.

01:00 The sample standard deviation, equals 26 .871, and we have that our confidence level or our alpha would be equal to, let's see here, our alpha would be 90%, or 0 .9 more accurately.

01:22 One moment here.

01:24 Actually, excuse me, let me correct myself here.

01:26 Our alpha value that we'd be looking for here is 0 .1, which means that to calculate our interval, we'd want to find z for 0 .05.

01:36 Which, using a z table, we'll find that that will be equal to one moment here.

01:42 All right, so we'll find z of 0 .05 equals 1 .64.

01:51 So our confidence interval then, where actually i'll note that our n equals 992, confidence interval is x bar plus or minus, z times s divided by the square root of n, which when we substitute in our values, we'll get that this becomes 67 .755 plus or minus 1 .399 or in terms of an interval, this would be about 66 .356 up to 69 .154...

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