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# Decision Rule

1) The restaurant chain claims that the waiting time of customers for service is normally distributed, with a mean of 3 minutes and a stdev of 1 minute. The quailty assurance department found in a sample of 50 customers at another place that the mean waiting time was 2.75 minutes. At a .05 significance level, can we conclude that the mean waiting times is less than 3 minutes?

2) The liquid chlorine added to swimming pools to combat algae has a relatively short shelf life before it loses its effectiveness. Records indicate that the mean shelf life of a 5 gallon jug of chlorine is 2,160 hours (90 days). As an experiment Holdlonger was added to the chlorine to find whether it would increase the shelf life. A sample of 9 jugs of chlorine had these shelf lives (in hours)
2159 2170 2180 2179 2160 2167 2171 2181 2185
At the .025 LOS, has Holdlonger increased the shelf life of the chlorine? Estimate the p-value.

3) A recent article in the WSJ reported that 30-year mortgage rate is now less than 6 percent. A sample of 8 small banks in the Midwest revealed the following 30-year rates (in percent)
4.8 5.3 6.5 4.8 6.1 5.8 6.2 5.6
At the .01 LOS, can we conclude that the 30-year mortgage rate for small banks is less than 6 percent? Estimate the p-value.

4) Given the following hypothesis:
Ho: u = 100
H1: u not equal to 100
A random sample of 6 resulted in the following values:
118, 105, 112, 119, 111
a) State the decision rule
b) Compute the value of the test stat
c) What is your decision regarding the null hypothesis
d) Estimate the p-value.

5) The management of white industries is consulting a new method of assembling its golf cart. The present method requires 42.3 minutes, on the average, to assemble a cart. The mean time for a random sample of 24 carts, using the new method, was 40.6 minutes and the stdev of the sample was 2.7 minutes. Using the .01 LOS, can we conclude that the assembly time using the new method is faster?

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