The population is normally distributed. A sample produces the following observat

Question

The population is normally distributed. A sample produces the following observations:

Use the critical value approach to conduct the test at a 1% level of significance. Use Table 2.

Find the mean and the standard deviation. (Round your intermediate calculations to 4 decimal places and final answers to 2 decimal places.)

Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Calculate the critical value of the test statistic. (Negative value should be indicated by a minus sign. Round your intermediate calculations to 4 decimal places and final answer to 3 decimal places.)

Explanation / Answer

a) Mean: 92.33 [(95+99+...+97)/6] and standard deviation: 7.89 [sqrt{1/6(95-92.33)^2+...+(97-92.33)^2}]

b) For small sample size, and knwon sample standard deviation, compute 1-sample t test.

t=(xbar-mu)/(s/sqrt n), where xbar is sample mean, mu is population mean, s is sample standard deviation and n is sample size.

=(92.33-100)/(7.89/sqrt 6)

=-2.38

c) The t5,0.01=-3.365 (left-tailed)

d) Option iv. [the test statistic do not fall in ritical region, therefore, do not reject null hypothesis]

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