Question 3

Surfer Dude Swimsuit Company plans to produce a new line of quick-dry swimsuits. Five textile companies are competing for the company’s quick-dry fabric contract. To check the fabrics of the five companies, Surfer Dude selected 10 random swatches of fabric from each company, soaked them with water, and then measured the amount of time (in seconds) each swatch took to dry when exposed to sun and a temperature of 80 F. The following table contains the amount of time (in seconds) each of these swatches took to dry. 

Company  Time in seconds

A 756 801 750 777 772 768 812 770 743 824 

B  791 696 761 760 741 810 770 823 815 845 

C 773 794 773 740 780 801 794 719 776 743 

D 760 723 699 756 834 791 742 739 801 724 

E 763 699 753 744 793 799 803 812 796 807 

You are required to conduct a hypothesis test using the ANOVA method to decide whether the mean drying times for all fabrics produced by the five companies are the same. Use excel to produce the ANOVA output. Note: Summit a copy of the ANOVA output with your answer.

a) Write the null and alternative hypotheses.

b) What are the degrees of freedom for the numerator and the denominator?

c) What are the values for the SSB, SSW, and SST.

d) Show the rejection and non-rejection regions on the F distribution for α = 0.05. Shade the rejection region.

e) Show the between-samples and within-samples variances.

f) From the ANOVA output calculate the MSB and MSW

g) What is the critical value of F for α = .05?

h) What is the calculated value of the test statistic F?

i) Will you reject the null hypothesis stated in part a) at a significance level of 5%? Give a complete statement pertaining to the decision.