Cross stitch is a needlecraft that merges sewing and embroidery using x- shaped stitches to form a pattern. According to a crafter at Malaysia art exhibition, a large (2 x 2 meters) cross stitch typically takes at least 31 months to stitch. The average amount of time spent by a group of 16 cross stitch crafters to complete one was 25 months, with a standard deviation of 7.2 months.

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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5. Cross stitch is a needlecraft that merges sewing and embroidery using x-
shaped stitches to form a pattern. According to a crafter at Malaysia art
exhibition, a large (2 x 2 meters) cross stitch typically takes at least 31 months
to stitch. The average amount of time spent by a group of 16 cross stitch
crafters to complete one was 25 months, with a standard deviation of 7.2
months.
a) Examine the crafter's claim by using a 2.5% significance level. Assume that
the time taken to finish a cross stitch is normally distributed for all cross stitch
crafters. [CO3, C4]
b) Describe the Type I error in part a). Present the probability of creating this
error. [CO2, A3 & A2]
c) Discuss your decision of part (a) if the probability of creating a Type I error
is 0.001. [CO3, C2]
Transcribed Image Text:5. Cross stitch is a needlecraft that merges sewing and embroidery using x- shaped stitches to form a pattern. According to a crafter at Malaysia art exhibition, a large (2 x 2 meters) cross stitch typically takes at least 31 months to stitch. The average amount of time spent by a group of 16 cross stitch crafters to complete one was 25 months, with a standard deviation of 7.2 months. a) Examine the crafter's claim by using a 2.5% significance level. Assume that the time taken to finish a cross stitch is normally distributed for all cross stitch crafters. [CO3, C4] b) Describe the Type I error in part a). Present the probability of creating this error. [CO2, A3 & A2] c) Discuss your decision of part (a) if the probability of creating a Type I error is 0.001. [CO3, C2]
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