A manufacturer wants to assess whether or not rods are being constructed appropr

Question

A manufacturer wants to assess whether or not rods are being constructed appropriately, where the diameter of the rods us supposed to be 1.0 cm, and the variation in the diameters is known to be distributed N(mu, 0.1). The manufacturer is willing to tolerate a deviation of the population mean from this value of no more than 0.1 cm, i.e., if the population mean is within the interval 1.0 plusminus 01. Cm, then the manufacturing process is performing correctly. A sample of n = 1.05 cm, with s^2 = 0.083 cm^2. Are these results statistically significant? Are the results practically significant? Justify your answers. A polling firm conducts a poll a determine what proportion theta of voters in a given population will vote in an upcoming election. A random sample of n = 205 was taken from the population, and the proportion answering yes was 0.62. Assess the hypothesis H_0: theta = 0.65 and construct an approximate 0.90-confidence interval for theta.

Explanation / Answer

6.3.8

alpha = 1 - 0.90 = 0.10

alpha / 2 = 0.05     Z = 1.64

I: 0.65 +/- 1.64 *SRQT[ (0.65*0.35) / 250 ]

0.65 +/- 0.0495

0.6005 < THETA < 0.6995

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