Ho: mean = 370
Ha: mean > 370
Z = (score-mean)/SEm = ?
SEm = SD/βn
Ha: mean > 370
Z = (score-mean)/SEm = ?
SEm = SD/βn
SE = Population Standard Deviation / Square Root of Sample Size
In this case, the population standard deviation (Ο) is $80, and the sample size (n) is 45.
Let's substitute these values into the formula to calculate the standard error:
SE = 80 / β45
SE β 11.97
The test value, also known as the z-score, can be calculated using the formula:
z = (sample mean - population mean) / SE
The population mean (ΞΌ) is given as $370, and the sample mean (xΜ) is $390. Substituting these values, along with the standard error, into the formula:
z = ($390 - $370) / 11.97
z β 1.67
Therefore, the test value for this hypothesis is approximately 1.67.
The formula for the test statistic, also known as the z-score, is given by:
z = (sample mean - population mean) / (population standard deviation / βsample size)
In this case, the population mean is $370, the population standard deviation is $80, and the sample size is 45. The sample mean is $390.
Plugging these values into the formula, we get:
z = ($390 - $370) / ($80 / β45)
Simplifying further:
z = $20 / ($80 / β45)
To calculate this, we first need to find the value of β45. Taking the square root of 45, we get approximately 6.7082.
Now, we can substitute this value into the formula:
z = $20 / ($80 / 6.7082)
z = $20 * (6.7082 / $80)
Simplifying further:
z β $20 * 0.08385125
z β 1.677025
Therefore, the test value for this hypothesis is approximately 1.677025.