suppose the alternative hypothesis in a hypothesis test is "the population mean is less than 60" if the sample size is 50 and alpha =.05, the critical value of the z is?
-1.96
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability
(p ≤ .05) and its Z score.
To find the critical value of the z in a hypothesis test, we need to first determine the significance level (alpha) and the type of test being conducted (one-tailed or two-tailed).
In this case, the alternative hypothesis states that the population mean is less than 60, indicating a one-tailed test. The significance level (alpha) is given as 0.05.
Since it is a one-tailed test, the critical value will be determined from the standard normal distribution table using the alpha value.
In a normal distribution, 0.05 is located in the lower tail (left side) of the distribution. Using a standard normal distribution table or a statistical software, we can find the z-value that corresponds to an area of 0.05 in the lower tail.
Checking the table or using a calculator, you will find that the critical value for alpha = 0.05 (in a one-tailed test) is approximately -1.645.
Therefore, the critical value of z for a hypothesis test with an alternative hypothesis that states "the population mean is less than 60," a sample size of 50, and an alpha level of 0.05 is approximately -1.645.
To find the critical value of the z for a hypothesis test, follow these steps:
Step 1: Determine the confidence level (1 - α).
In this case, α = 0.05, which means a 95% confidence level because alpha (α) is the level of significance, and we subtract it from 1 to get the confidence level.
Step 2: Find the critical value for the given confidence level.
Since the alternative hypothesis is "the population mean is less than 60," and we are using a z-test, we need to find the critical z-value from the standard normal distribution table.
For a 95% confidence level, half of the area (0.05) is in the left tail of the distribution. You need to find the z-score that corresponds to this tail area.
Referencing the standard normal distribution table, look for an entry closest to a cumulative probability of 0.05. The entry closest to 0.05 is at the row labeled 1.6 and column labeled 0.05.
The critical value is -1.645 according to the standard normal distribution table for a 95% confidence level (α = 0.05).
Thus, the critical value of z for this hypothesis test is -1.645.