Consider the following hypothesis test: H 0: 50 H a: > 50 A sample of 50 is used and the population standard deviation is 9. Use the critical value approach to state your conclusion for each of the following sample results. Use = .05.
a. With = 52.5, what is the value of the test statistic (to 2 decimals)? Can it be concluded that the population mean is greater than 50?
b. With = 51, what is the value of the test statistic (to 2 decimals)? Can it be concluded that the population mean is greater than 50?
c. With = 51.8, what is the value of the test statistic (to 2 decimals)? Can it be concluded that the population mean is greater than 50?
For 0.05 significance level and 0.05 significance level, Critical z value = 1.645
Hence,
Rejection region will be z > 1.645
a) Test statistic
= 1.96
Since test statistic is greater than 1.645, we reject Ho and we can conclude that population mean is greater than 50.
b) Test statistic
= 0.79
Since test statistic is not greater than 1.645, we fail to reject Ho and we can't conclude that population mean is greater than 50.
c) Test statistic
= 1.41
Since test statistic is not greater than 1.645, we fail to reject Ho and we can't conclude that population mean is greater than 50.
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