Question

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99. Whozi-whatzits are supposed to have ramfluke densities below 75. A new process for manufacturing whozi-whatzits is being tested. The ramfluke densities of a random sample of ten whozi-whatzits (produced using the new process) were recorded as 74.6, 75.1,74.9, 75.2, 74.3, 74.9,75.3, 74.8, 75.5, 77.8. State the appropriate null and alternative hypotheses. Find upper and lower bounds on the P-value. Should the new process be implemented? For the problems, you may assume that ramfluke densities of whozi- whatzits produced using the new process are approximately normally distributed. a. b.

Answer 1

a) H₀: $\mu$> 75

   H₁: $\mu$ < 75

b) $\bar x$ = 75.24

    s = 0.9642

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

                             = (75.24 - 75)/(0.9642/$\sqrt 10$)

                            = 0.787

P-value = P(T < 0.787)

            = 0.7742

0.500 < P-value < 1.000

At alpha = 0.05, since the P-value is greater than the significance level(0.7742 > 0.05), so we should not reject the null hypothesis.

No, the new process should not be implemented.