Find the value of x.
1 answer:
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Answer:
(a) Yes, there is evidence that the water temperature is acceptable at (b) 0.9987 (c) 6.647274e-06
Step-by-step explanation:
Let X be the random variable that represents the water temperature. The water temperature has been measured on n = 9 randomly chosen days (a small sample), the sample average temperature is = 100°F and
= 2°F. We suppose that X is normally distributed.
We have the following null and alternative hypothesis
vs
(upper-tail alternative)
We will use the test statistic
and the observed value is
.
(a) The rejection region is given by RR = {z | z > 1.6448} where 1.6448 is the 95th quantile of the standard normal distribution. Because the observed value -3 does not belong to RR, we fail to reject the null hypothesis. In other words, there is evidence that the water temperature is acceptable at .
(b) The p-value for this test is given by P(Z > -3) = 0.9987
(c) P(Accepting when
) = P(The observed value is not in RR when
) = P(
< 1.6448 when
) = P(
< 102 + (1.6448)(
) when
) = P(
< 103.0965) when
) = P(
)) = P(Z < -4.3552) = 6.647274e-06