A student competition involves building a scale model of a multistory structure out of

balsa wood and then subjecting it to seismic loading on a shake table and observing its

behavior. Balsa wood comes in $3$ standard densities:

For all of problem $1$ questions, the standard deviation of the measurement technique is

$3\mathrm{.}2l\frac{b}{f}{t}^3$

Problem $1$a$)$

What is the probability of measuring a density of $10\mathrm{.}2l\frac{b}{t}{t}^3$ or greater if the students

have low density balsa wood? Assume the data is normally distributed.

$0\mathrm{.}098$

$0\mathrm{.}246$

$0\mathrm{.}902$

$0\mathrm{.}754$

Problem $1$b$)$

What is the probability of measuring $4$ samples and getting an average density of $10\mathrm{.}2l\frac{b}{f}{t}^3$ or

greater if the students have low density balsa wood? Assume the data is normally distributed.

$0\mathrm{.}085$

$0\mathrm{.}097$

$0\mathrm{.}915$

$0\mathrm{.}246$

Problem $1$c$)$

The students measure the density of $4$ samples and calculate an average of $10\mathrm{.}2l\frac{b}{t}{t}^3.$ What is

the $95\%2-$sided confidence interval range. Use a normal distribution for your calculations.

$(7\mathrm{.}3,12\mathrm{.}2)$

$(7\mathrm{.}1,13\mathrm{.}3)$

Problem $1$d$)$

The students measure the density of $4$ samples and determine an average of $10\mathrm{.}2l\frac{b}{t}{t}^3.$ What

is the $95\%2-$sided confidence interval range? Given the small sample size, use the t$-$

distribution.

$(7\mathrm{.}0,13\mathrm{.}4)$

$(5\mathrm{.}1,15\mathrm{.}3)$

$(9\mathrm{.}7,10\mathrm{.}7)$

$(2\mathrm{.}3,18\mathrm{.}1)$

Problem $1$e$)$

One of the students involved in the project believes they accidentally ordered high density balsa

wood $(16l\frac{b}{t^3})$ instead of low density $(8l\frac{b}{t^3}).$ The student writes the following hypotheses:

Based on the data they collected $(4$ samples, average $10\mathrm{.}2l\frac{b}{t^3},$ standard deviation $3\mathrm{.}2l\frac{b}{t}{t}^3),$

what is the p$-$value calculated from hypothesis testing using the $t-$distribution?

$0\mathrm{.}036$

$0\mathrm{.}0003$

$0\mathrm{.}050$

$0\mathrm{.}982$

Problem $1$f$)$

Which is the most accurate conclusion we can make from the hypothesis testing in $1$eif we use

a $0\mathrm{.}05$ significance?

The wood is unlikely to be low density balsa wood.

The wood is likely to be medium density balsa wood.

The wood is likely to be high density balsa wood.

The wood is unlikely to be high density balsa wood.