Question

1. The following scenarios each contain enough information to carry out a hypothesis test for means. For each one, (1) give the formula for the test statistic (in terms of the variables, not the numbers in the problem!), (2) indicate which distribution you would use to determine the critical value, and (3) give the number of degrees of freedom, either as a formula or as calculated for the problem (if relevant). You don’t have to explain your answers, and you don’t have to solve the problems.

2. (a) Droidsmiths find that extracting memories from droids takes .24 ms on average. One contrarian droidsmith on Kijimi claims this isn’t so because in its past 42 memory extractions, it has calculated its average time to be .39 ms and its standard deviation to be .08 ms. Test this droidsmith’s claim at a significance level of α = .01138.

3. (b) The mean distance of a hyperspace jump enabled by a Sith wayfinder is often whispered to be 3.4 parsecs, but Rey discovered that the mean distance of the 17 jumps she made on her way to Exegol was 3.95 parsecs and that her jump distances were normally distributed. An ancient technical manual for Sith wayfinders states that the standard deviation for such a distance is .94 parsecs. Test the hypothesis that the mean distance of such a jump is greater than 3.4 parsecs given α = .02.

4. (c) Biologists have long thought the mean size of a murder of Porgs is 136.7; in an study of 11 Porg colonies, the mean murder size was determined to be 112.4 and the standard deviation of the murder size was determined to be 30.3.1 Test the hypothesis that the mean size of a murder of Porgs is less than 136.7 given α = .03.

5. (d) The mean length of a lightsaber hilt is supposedly 10.5 inches, but some suspect that this is due to rounding to Earth Imperial units. Researchers carry out a secret study of 59 lightsaber hilts and find that their mean length is 10.24 inches; they have noted that the data is roughly normally distributed but rely on a previous study’s standard deviation of 1.2 inches when they test this hypothesis for α = .05.

Answer 1

(a)(1)

(2)

t distribution

(3)

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(b)(1)

(2)

Standard normal distribution

(3)

Degree of freedom not required.

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(c)(1)

(2)

t distribution

(3)

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(d)(1)

(2)

Standard normal distribution

(3)

Degree of freedom not required.

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