# Stat 2507 Assignment 3

STAT 2507 Fall 2013 Total of marks=100. Every question is worth 4 marks . Part I. Lab Questions. Use only the blanks left to answer lab questions. Print all histograms, boxplots, stem-and-leaf plots, etc, you are asked to generate. 1. (Service times) To decide on the number of service counters needed for stores to be built in future, a supermarket chain wanted to obtain information on the length of time (in minutes) required to service customers. To ﬁnd the distribution of such time, a sample of 60 customers service times was recorded (see the ﬁrst column in the Excel ﬁle). You are asked to copy and paste data in this column in a minitab spreadsheet (that you have to open ﬁrst). (a) Construct a stem-and-leaf plot for the data by clicking Graph → Stem-and-Leaf . (b) What is the customer’s service median time? median=1.2 (c) What fraction of the service times are less than or equal to 1 min? 24/60 (d) What are the smallest and the largest service times? 0.2 and 5.2 (e) Third of the service times are above what value? Q 3 = 2 . 4 2. (Service times, continued.) (a) Construct a dotplot for the data above by clicking Graph → Dotplot → Simple .

MTB>random 9 c1-c20;SUBC>normal 68.71 3.MTB>tinterval 0.90 c1-c20a.[2] How many of your intervals containμ? 17 (any number greater than 14 is acceptable.b.Would you expect all 20 of the intervals to containμ? [0.5]No. Why? Expected is(20)(0.90)=18 [1.5]c.Do all the intervals have the same width? [1]No. Why (what is the theoretical width)?2(t0.05)s/√nwheresis changed from sample to sample. [1]d.[1] Suppose you took 95% intervals instead of 90%. Would they be narrower or wider?Widere.[2] How many of your intervals contain the value 71? 6, but any number between 5 and16 is acceptable.f.Suppose you took samples of sizen= 64 instead ofn= 9. Would you expect more orfewer intervals to contain 71? [1] Fewer. What about 68.71? Same[1] What about the widthof the intervals forn= 64: Would they be narrower or wider than forn= 9? [1] Narrower.3.Hypothesis testing forμwhenσis knownImaging choosingn= 16 women at random from a large population and measuring theirheights. Assume that the heights of the women in this population are normal withμ= 63.8inches andσ= 3 inches. Suppose you then test the null hypothesisH0:μ= 63.8 versus thealternative thatHa:μ6= 63.8, usingα= 0.10. Assumeσis known. Simulate the results ofdoing this test 30 times as follows:MTB>random 16 c1-c30;SUBC>normal 63.8 3.MTB>ztest 63.8 3 c1-c30a.[2] In how many tests did you rejectH0. That is, how many times did you make an“incorrect decision”? I had 3 p-values less than 0.10, but any number≤8 is acceptable.

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