Question

Pedego Electric Bikes manufactures and sells its own brand of electric bicycles (Ebike). The company is based in Irvine, California. The bicycles can be pedaled manually and also be powered electrically, reaching speeds of up to 20 miles per hour. One model in Pedego’s line is the “Comfort Cruiser Ebike”. Based on historical production records, it took 47 minutes, on average, to completely assemble a Comfort Cruiser Ebike.

Pedego has recently instituted some major technological innovations to their assembly line and wants to know whether there has been a significant change in the average assembly time for the Comfort Cruiser Ebike. After the innovations had been in place for one month, the production manager took a random sample of 19 Comfort Cruisers from the assembly line and recorded the amount of time it took to completely assembly each one – the sample mean and standard deviation were 45 minutes and 3.63 minutes, respectively.

Can Pedego’s production manager conclude that the technological innovations made to the assembly line have significantly changed the average assembly time of the Comfort Cruiser Ebike? Do a complete and appropriate hypothesis test, using a significance level of .02.

Step 1 (Hypotheses)

H₀:   (Click to select)  n  μ  p  x-bar  s  π  σ     (Click to select)  =  ≠  ≤  >  ≥  <    

H_A:   (Click to select)  μ  x-bar  π  p  σ  s  n     (Click to select)  =  ≠  ≤  >  ≥  <    

Step 2 (Decision rule)

Using only the appropriate statistical table in your textbook, the critical value for rejecting H₀ is  (Click to select)  +  -  ±   . (report your answer to 3 decimal places, using conventional rounding rules)

Step 3 (Test statistic)

Using the sample data, the calculated value of the test statistic is  (Click to select)  +  -  ±   . (report your answer to 2 decimal places, using conventional rounding rules)

Step 4 (Evaluate the null hypothesis)

Should the null hypothesis be rejected?   (Click to select)  yes  no   

Step 5 (Practical conclusion)

Can Pedego’s production manager conclude that the technological innovations made to the assembly line have significantly changed the average assembly time of the Comfort Cruiser Ebike?   (Click to select)  yes  no   

Using only the appropriate statistical table in your textbook, what is the most accurate statement you can make about the numerical value of the p-value of this hypothesis test?       

Answer:  (provide a one-sentence statement about the p-value)

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 47
Alternative Hypothesis, Ha: μ ≠ 47

Rejection Region
This is two tailed test, for α = 0.02 and df = 18
Critical value of t are -2.552 and 2.552.
Hence reject H0 if t < -2.552 or t > 2.552

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (45 - 47)/(3.63/sqrt(19))
t = -2.40

no

no   

P-value Approach
P-value = 0.0273
As P-value >= 0.02, fail to reject null hypothesis.