It is claimed that a vacuum cleaner expends 46 kWh per year. A random sample of

Question

It is claimed that a vacuum cleaner expends 46 kWh per year. A random sample of 12 homes indicates that vacuum cleaners expend an average of 42 kWh per year with sample standard deviation 11.9 kWh. Does this suggest that, on average, vacuum cleaner expend less than 46 kWh per year? Assume the population to be normally distributed. State the appropriate null and alternative hypotheses? Compute the value of the test statistics. Compute the p-value. State your conclusion in words. Use a significance level of 0.05.

Explanation / Answer

a) H0:mu>=46 KWh (vaccum cleaner expends atleast 46 kwh per year)

H1:mu<46 KWh  (vaccum cleaner expends less than 46 kwh per year)

b) Perform 1-sample t test(sample size<30, sample standard deviation is knwon)

t=(Xbar-mu)/(s/sqrt n)

=(42-46)/(11.9/sqrt 12)

=-1.16

c) p value is:0.1353

d) The p value is not less than alpha=0.05. Fail to reject H0, insufficient sample evidence to cocnlud ethat vaccum cleaner expends less than 46 kwh per year.

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