A manufacturer of toasters claims that the toasters have a mean life of 9 years

Question

A manufacturer of toasters claims that the toasters have a mean life of 9 years and a standard deviation of 2.1 years. A random sample of 60 such toasters is selected for testing. If the sample produces a mean value of 8.3 years, is there sufficient evidence that the mean toaster life is less than the manufacturer claimed?

Question 2 options

: 1) One sample z-test for the population mean.

2) two sample z-test for the population means.

3) One sample z-test for proportions.

4) two sample z-test for proportions.

5) one sample t-test for the population mean.

6) None of our hypothesis tests fit.

Explanation / Answer

here as std deviaiton ls known:

: 1) One sample z-test for the population mean.

here std error =std deviiton/(n)1/2 =2.1/(60)1/2 =0.271

therefore test statistic z=(X-mean)/std error =(8.3-9)/0.271 =-2.582

for above test statiistc p value = 0.0049

as p value is significantly low we reject null hypothesis and conclude that there is sufficient evidence that the mean toaster life is less than the manufacturer claimed

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