Question

The workweek for adults in the US that work full time is normally distributed with a mean of 47 hours. A newly hired engineer at a start-up company believes that employees at start-up companies work more on average than working adults in the US. She asks 15 engineering friends at start-ups for the lengths in hours of their workweek. Their responses are shown in the table below. Test the claim using a 1% level of significance. See Excel for Data (42 45 46 46 48 48 49 49 50 52 53 54 54 55 55) workweek hour data.xlsx The hypotheses for this problem are: H0: μ = 47 H1: μ > 47 Find the p-value. Round answer to 4 decimal places. p-value

Answer 1

To test the claim, we will conduct a hypothesis test using a 1% level of significance. The p-value of approximately 0.0163 is less than the significance level of 0.01. Therefore, we reject the null hypothesis. There is sufficient evidence to support the claim that employees at start-up companies work more on average than working adults in the US.

Step-by-step explanation:

Testing the Claim

To test the claim, we will conduct a hypothesis test using a 1% level of significance. The null hypothesis (H0) is that the mean workweek for employees at start-up companies is equal to the mean workweek for working adults in the US, which is 47 hours. The alternative hypothesis (H1) is that the mean workweek for employees at start-up companies is greater than 47 hours.

Calculating the Test Statistic

1. Calculate the sample mean of the engineering friends' workweek hours.

The sample mean is 49.

2. Calculate the sample standard deviation of the engineering friends' workweek hours.

The sample standard deviation is approximately 4.43.

3. Calculate the test statistic using the formula: test statistic = (sample mean - population mean) / (sample standard deviation / sqrt(sample size)).

In this case, the test statistic is (49 - 47) / (4.43 / sqrt(15)) ≈ 2.15.

Calculating the p-value

4. Use the test statistic to calculate the p-value.

The p-value represents the probability of obtaining a test statistic as extreme as the one calculated, assuming the null hypothesis is true.

In this case, we are conducting a one-tailed test, so we will look for the area under the normal distribution curve to the right of the test statistic.

5. Using a standard normal distribution table or a calculator, the p-value is approximately 0.0163.

Conclusion

The p-value of approximately 0.0163 is less than the significance level of 0.01.

Therefore, we reject the null hypothesis. There is sufficient evidence to support the claim that employees at start-up companies work more on average than working adults in the US.