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From his stock of engines, the inventor selects a simple random sample of 50 engines for testing. The engines run for an average of 305 minutes. The true standard deviation is known and is equal to 30 minutes, and the run times of the engines are normally distributed. In R-studio, test the hypothesis that the mean run time is more than 300 minutes. Use a 0.01 level of significance.

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princessesther2011

Answer:

The mean run time of the engines is greater than 300 minutes

Step-by-step explanation:

Null hypothesis: The mean run time of the engines is 300 minutes.

Alternate hypothesis: The mean run time of the engines is greater than 300 minutes.

Test statistic (Z) = (sample mean - population mean) ÷ sd/√n

sample mean = 305 minutes

population mean = 300 minutes

sd = 30 minutes

n = 50

Z = (305 - 300) ÷ 30/√50 = 5 ÷ 4.243 = 1.178

The test is a one tailed test. Using a 0.01 significance level, the critical value which is obtained from the standard normal distribution table is 2.326.

Conclusion:

Since the test statistic 1.178 is less than the critical value 2.326, reject the null hypothesis.

There is sufficient evidence to support the claim that the mean run time is more than 300 minutes.