Quiz 7 Key
MA 223
1. We would take H0 : µ = 375 versus Ha : µ ̸= 375, where µ is the
population mean for all of the bulbs in the shipment.
x̄−375
√
2. Under H0 we find that Z = s/
is standard normal, and so with
100
probability 0.95 we will have −1.96 < Z < 1.96 for an IID sample of
350−375
√
100 bulbs. In our case Z = 100/
= −2.5, outside the range required.
100
We reject H0 .
The p-value for this two-sided test is p = 0.0124.
3. Circle true or false:
TRUE: In part (2) we could have made a type I error (since we
may have erroneously rejected H0 ).
FALSE: In part (2) we could NOT have made a type II error
(that means accepting H0 when in fact H0 is false).
FALSE: If we decrease α the probability of making a type II error
cannot decrease, and will likely increase.
1