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1 Bidri

The production of Bidri is a traditional craft of India. Bidri wares (bowls, vessels, and so on) are cast from an alloy containing primarily zinc along with some copper. Consider the observations on copper content (%) for a sample of Bidri artifacts in London’s Victoria and Albert Museum, contained in http://ritsokiguess.site/datafiles/bidri.csv.

(1 point) Read in and display (some of) the data.

(2 points) Make a suitable plot to assess whether these values come from a normal distribution.

(2 points) What do you conclude about normality from your plot? (I see two pieces of relevant evidence.)

(2 points) Why do you think a researcher would favour a sign test over a t
t
-test for these data? Explain briefly.

(3 points) The copper content of other Bidri ware has been found to be 4 (percent). Test whether the Bidri ware that ended up at this museum comes from a population with a different median percentage of copper. What do you conclude, in the context of the data?

(2 points) Find a 90% confidence interval for the median copper content (of the artifacts from which these are a sample).

(4 points) Estimate (by simulation) and plot the bootstrap sampling distribution of the sample mean for these data, and explain why this offers further support for not doing a t
t
-test here.

2 Spatial perception

Twenty-six neurologically impaired children have each taken two tests of spatial perception, called “A” and “B”. We want to find out whether the scores on the two tests are similar or definitely different. The data are in http://ritsokiguess.site/datafiles/spatial.csv.

(1 point) Read in and display (some of) the data.

(2 points) Why is this matched pairs data?

(3 points) Make a graph that is suitable for assessing the assumptions of the matched-pairs t
t
-test.

(2 points) How would you justify doing a matched-pairs t
t
-test for comparing the two assessments of spatial awareness, rather than a matched-pairs sign test?

(3 points) Carry out a matched-pairs t
t
-test to assess whether there are any differences in mean scores between tests A and B. What do you conclude, in the context of the data?

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