In: Statistics and Probability
1. For the standardized test statistic approach to hypothesis testing, calculate the test statistic for testing the null hypothesis that the population mean is less than or equal to 9.29, given a sample mean of 13.90, a sample size of 35, and a population standard deviation of 3.92. Round to two decimals.
2. Using the traditional hypothesis testing approach, calculate
the critical value for testing the null hypothesis that the
population mean is greater than or equal to 13,
given a sample size of 48, a population standard
deviation 5.23, and a significance level of
0.05. Round to two decimals.
K = ?
Solution :
1) The null and alternative hypothesis is ,
H0 : = 9.29
Ha : < 9.29
= 13.90
= 3.92
n = 35
Test statistic = z =
= ( - ) / / n
= (13.90 - 9.29) / 3.92 / 35
Test statistic = z = 6.96
2) The null and alternative hypothesis is ,
H0 : = 13
Ha : > 13
= 5.23
n = 48
= 0.05
This is the right tailed test,
P(z > z ) = 0.05
= 1 - P(z < z ) = 0.05
= P(z < z ) = 1 - 0.05
= P(z < z ) = 0.95
= P(z < 1.65 ) = 0.95
K = 1.65