Question

The mean work week for engineers in a start-up company is believed to be about 60 hours. A newly hired engineer hopes that it's shorter. She asks 10 engineering friends in start-ups for the lengths of their mean work weeks. Based on the results that follow, should she count on the mean work week to be shorter than 60 hours? Conduct a hypothesis test at the 5% level. Data (length of average work week): 70; 50; 60; 65; 65; 60; 55; 55; 55; 60. Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

Part (b) State the alternative hypothesis. Ha: μ = 60 Ha: μ ≠ 60 Ha: μ < 60 Ha: μ > 60 Incorrect: Your answer is incorrect

Part (d) State the distribution to use for the test. (Enter your answer in the form z or tdf where df is the degrees of freedom.)

Part (e) What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.) ---Select--- =

Part (f) What is the p-value? (Round your answer to four decimal places.) Explain what the p-value means for this problem. If H0 is false, then there is a chance equal to the p-value that the average work week for engineers in a start-up business is the mean of the sample or less. If H0 is true, then there is a chance equal to the p-value that the average work week for engineers in a start-up business is the mean of the sample or less. If H0 is false, then there is a chance equal to the p-value that the average work week for engineers in a start-up business is not the mean of the sample or less. If H0 is true, then there is a chance equal to the p-value that the average work week for engineers in a start-up business is not the mean of the sample or less.

Part (g) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot

Part (h) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.

(i) Alpha (Enter an exact number as an integer, fraction, or decimal.) α =

(ii) Decision: reject the null hypothesis do not reject the null hypothesis

(iii) Reason for decision: Since α > p-value, we reject the null hypothesis. Since α < p-value, we reject the null hypothesis. Since α > p-value, we do not reject the null hypothesis. Since α < p-value, we do not reject the null hypothesis.

(iv) Conclusion: There is sufficient evidence to conclude that the average number of hours engineers work each week is less than 60 hours. There is not sufficient evidence to conclude that the average number of hours engineers work each week is less than 60 hours.

Part (i) Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your lower and upper bounds to two decimal places.) WebAssign Plot

Answer 1

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