Question

1. an article in a business magazine reports that 24% of full - time remote workers feel they would be more productive if they did not work remotely. a researcher has reason to doubt this claim and surveys a random sample of 600 remote workers. a total of 168 of these surveyed workers say they believe they would be more productive if they did not work remotely. the researcher calculates the test statistic for her hypothesis test as shown below. what is wrong with the researchers calculations? i ( z=\frac{0.28 - 0.24}{sqrt{\frac{0.24(1 - 0.24)}{600}}}approx2.3 ) a. nothing is wrong with these calculations. b. the sample proportion was computed incorrectly. c. the test statistic should be negative. d. the standard error does not include the correct values. e. the test statistic should be larger.

Explanation:

Step1: Calculate the sample proportion

The sample proportion $\hat{p}$ is calculated as $\hat{p}=\frac{x}{n}$, where $x = 168$ (number of successes) and $n=600$ (sample size). So, $\hat{p}=\frac{168}{600}=0.28$.

Step2: Analyze the formula for the test statistic

The formula for the $z -$ test statistic for a proportion is $z=\frac{\hat{p}-p}{\sqrt{\frac{p(1 - p)}{n}}}$, where $p = 0.24$ (population proportion), $\hat{p}=0.28$, and $n = 600$. Substituting the values: $z=\frac{0.28 - 0.24}{\sqrt{\frac{0.24(1 - 0.24)}{600}}}$.
The numerator is positive ($0.28-0.24 = 0.04>0$), so the $z -$ statistic should be positive.

Answer:

A. Nothing is wrong with these calculations.