Surfer Dude swimsuit company plans to produce a new line of quick-dry swimsuits. Four textile companies are competing for the company’s quick-dry fabric contract. To check the fabrics of the four 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 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 four companies are the same. You can use either excel or formulae to answer this question. Note: If using excel, 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) Calculate SSB, SSW, and SST. d) Show the rejection and non-rejection regions on the F distribution curve for α = .01. e) Calculate the between-samples and within-samples variances. f) What is the critical value of F for α = .01? g) What is the calculated value of the test statistic F? h) Will you reject the null hypothesis stated in part a) at a significance level of 1%?
Surfer Dude swimsuit company plans to produce a new line of quick-dry swimsuits. Four textile companies are competing for the company’s quick-dry fabric contract. To check the fabrics of the four 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
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 four companies are the same. You can use either excel or formulae to answer this question. Note: If using excel, 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) Calculate SSB, SSW, and SST.
d) Show the rejection and non-rejection regions on the F distribution curve for α = .01.
e) Calculate the between-samples and within-samples variances.
f) What is the critical value of F for α = .01?
g) What is the calculated value of the test statistic F?
h) Will you reject the null hypothesis stated in part a) at a significance level of 1%?
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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
A 756
B 791
C 773
D 760
E 763
Time in seconds
801 750 696 761 794 773 723 699 699 753
777 772 760 741 740 780 756 834 744 793
768 812 810 770 801 794 791 742 799 803
770 743 824 823 815 845 719 776 743 739 801 724 812 796 807
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?
by Bartleby ExpertSurfer 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.
by Bartleby Expert
