2.2.21 Consider the investigation of the manufacturing

process that is producing hypodermic needles. Recall that the

most recent random sample of 35 needles have an average

diameter of 1.64 mm and a standard deviation of 0.07 mm.

a. Use the Theory-Based Inference applet to fi nd and report

a standardized statistic (t-statistic) and a p-value to investigate

whether the average diameter of needles produced

by this manufacturing process is different from 1.65 mm.

b. Based on your p-value, write out a conclusion, being sure

to include justification.

2.2.7 An instructor collected data on the number of states

students in her class have visited in the U.S. A dotplot for the

collected data is shown below.

a. Identify the observational units.

b. Identify the variable recorded and whether it is categorical

or quantitative.

c. Describe what the graph tells us about distribution of the

variable recorded. Be sure to comment on shape, center,

and variability.

d. Use the dotplot to find and report the median value for

the number of states visited by the students in this study.

e. Would the mean value for these data be smaller than,

larger than, or the same as the median, as reported in (d)?

Explain your reasoning.

f. Suppose that the observation recorded as 43 states is a

typo and was meant to be 34. If we corrected this entry in

the data set, how would the following numerical statistics

change, if at all?

Mean: Smaller Same Larger

Median: Smaller Same Larger

Standard deviation: Smaller Same Larger