As part of the quality-control program for a catalyst manufacturing line, the raw materials (alumina and a binder) are tested for purity. the process requires that the purity of the alumina be greater than 85%. a random sample from a recent shipment of alumina yielded the following results (in percent):
93.2 87.0 92.1 90.1 87.3 93.6
a hypothesis test will be done to determine whethe or not to accept the shipment.

(a) state the appropriate null and alternate hypotheses.
(b) compute the p-value.
(c) should the shipment be accepted? explain.

We accept the alternate hypothesis that the purity of the alumina is greater than 85% and hence, the shipment should be accepted.          

Step-by-step explanation:

We are given the following in the question:  

93.2, 87.0, 92.1, 90.1, 87.3, 93.6

Formula:

where are data points, is the mean and n is the number of observations.  

Sum of squares of differences = 7.0225 +12.6025 + 2.4025 + 0.2025 + 10.5625 + 9.3025 = 42.095

Sample size, n = 6

Alpha, α = 0.05

First, we design the null and the alternate hypothesis

We use One-tailed t test to perform this hypothesis.

Formula:

Putting all the values, we have

The p-value is 0.003969.

Since, p-value < 0.05

We reject the null hypothesis and fail to accept it.

We accept the alternate hypothesis that the purity of the alumina is greater than 85% and hence, the shipment should be accepted.

126.66 m²

step-by-step explanation:

the pertinent area formula is a = πr², where r is the radius.

here, a = π(6.35 m)² = 40.32π, or approximately 126.66 m²