Question

Problem 3-24 points You're a quality control engineer at Tinker Air Force Base, and you're worried that a subassembly for certain aircraft weighs too much (and is therefore affecting the performance of the aircraft), You want the subassembly to weigh less than 45 pounds on average or you'll need to change suppliers of the subassembly. To test whether the average weight is less than 45 pounds, you weighed 16 different subassemblies, resulting in an average of 43.2 pounds and a standard deviation of 4.8 pounds a. Test the appropriate hypotheses with the critical value approach at α = 0.01. (10 points) a. test statistic critical value(s) 2 662 conclusion w.r.t. Ho b. What is the probability that you conclude that supplier changes are needed when the actual mean weight of the subassembly is 40 pounds? (14 pounds) ol 45 18 -10 is 15,a2 4O 12 IS O f セラー b.

Answer 1

a) H₀: $\mu$ = 45

    H₁: $\mu$ < 45

The test statistic t = ($\bar x - \mu$)/(s/$\sqrt n$)

                            = (43.2 - 45)/(4.8/sqrt(16))

                            = -1.5

At $\alpha$ = 0.01, the critical value is t_0.01,15 = -2.602

Since the test statistic value is not less than the critical value(-1.5 > -2.602), so we should not reject H₀.

b) t_crit = -2.602

or, ($\bar x$_crit - $\mu$)/(s/$\sqrt n$) = -2.602

or, ($\bar x$_crit - 45)/(4.8/sqrt(16)) = -2.602

or, $\bar x$ _crit = -2.602 * (4.8/sqrt(16)) + 45

or, $\bar x$ _crit = 41.8776

$\beta$ = P($\bar x$ > 41.8776)

    = P(($\bar x$ - $\mu$)/(s/$\sqrt n$) > (41.8776 - $\mu$)/(s/$\sqrt n$))

    = P(T > (41.8776 - 40)/(4.8/sqrt(16)))

    = P(T > 1.56)

   = 1 - P(T < 1.56)

   = 1 - 0.9302

   = 0.0698