The mean work week for engineers in a start-up company is believed to be about 60 hours, on average. A newly hired engineer hopes that it's shorter. She asks ten engineering friends in start-ups for the lengths of their mean work weeks. The sample average was 58.1 hours and the standard deviation was 3.4 hours. Should she count on the mean work week to be shorter than 60 hours? Conduct a hypothesis test at the 5% significance level. Show all steps of the test.
Added by Mario G.
Step 1
Null hypothesis (H₀): The mean work week for engineers in a start-up company is 60 hours. H₀: μ = 60 Alternative hypothesis (H₁): The mean work week for engineers in a start-up company is less than 60 hours. H₁: μ < 60 Show more…
Show all steps
Close
Your feedback will help us improve your experience
Madhur L and 69 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
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 ten 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? Data (length of mean work week): 70; 45; 55; 60; 65; 55; 55; 60; 50; 55.
Hypothesis Testing with One Sample
Additional Information and Full Hypothesis Test Examples
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 ten engineering friends in start-ups for the lengths of their work weeks. Based on the random results that follow, should she count on the mean work week to be shorter than 60 hours? Use a 0.05 significance level to test this claim. Assume that lengths of work weeks are normally distributed. Data (length of mean work week, in hours): 70 45 55 60 65 55 55 60 50 55 1: Determine the hypotheses and significance level. H0: _____________ Ha: _____________ α = __________ 2: Check conditions. 3: Compute the sample test statistic. 4: Calculate the P-value using TI-84 or Excel. Then make a decision about the null hypothesis. 5: Interpret the conclusion.
Adi S.
The mean work week for engineers in start-up companies is claimed to be about 62 hours. Kara, a newly hired engineer hopes that it's not (she wants it to be shorter). She asks 10 engineers in start-ups for the lengths of their mean work weeks. Their responses are 70; 45; 55; 60; 65; 55; 55; 60; 50; 55. a. Is the newly hired engineer testing a mean or a proportion? mean proportion b. The null hypothesis (or company claim), in symbols, is μ = c. If the claim is correct, what is the probability that a sample mean would be as low as Kara's mean? % Give your answer as a percentage accurate to one decimal place. d. If Kara will accept the 62 hours as the real average so long as there's at least a 10% chance the sample average value could be as low as hers, should she accept the claim? yes no
Madhur L.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD