Find the P-value for a left tailed hypothesis test with a test statistic of z= -1.77. Decide wether to reject the null if the level of significance is alpha= 0.05.
Please help I've tried everything and I can't figure out how to get the right answer..
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability of Z = -1.77. Is the probability in the smaller area < .05?
To find the p-value for a left-tailed hypothesis test, you need to compare the absolute value of your test statistic (z= -1.77 in this case) with the standard normal distribution. The p-value represents the probability of observing a test statistic as extreme as the one obtained, assuming the null hypothesis is true.
To find the p-value:
1. Look up the corresponding critical value in the standard normal distribution table. Since it's a left-tailed test, we are interested in the area to the left of the test statistic.
2. Calculate the area to the left of the test statistic using the standard normal distribution table or software.
The critical value represents the value at which the p-value crosses the desired level of significance (alpha). If the absolute value of the test statistic is smaller than the critical value, the p-value will be greater than alpha, and you will fail to reject the null hypothesis. If the absolute value of the test statistic is greater than the critical value, the p-value will be less than alpha, and you will reject the null hypothesis.
For an alpha level of 0.05, the corresponding critical value can be found by looking up the area to the left of 0.05 in the standard normal distribution table. The critical value for alpha= 0.05 is approximately -1.645.
Next, compare the absolute value of your test statistic (|-1.77| = 1.77) with the critical value (-1.645). Since the absolute value of the test statistic is greater than the critical value, the p-value will be less than 0.05 (alpha).
Thus, in this case, you would reject the null hypothesis at the 0.05 level of significance because the p-value is less than alpha.