If you test the (one sample) null hypothesis that the population proportion p ¡Ü 0.3 and you get the test statistic value of z = -0.98, then using a 5% ignificance level, Question 18 options:
the alternative hypothesis looks believable.
the null hypothesis looks believable.
the null and alternative hypotheses both look believable.
none of the above.
With Z = -.98, that is not even one standard deviation below the mean.
The null hypothesis looks believable.
Well, with a test statistic of z = -0.98, it looks like our hypothesis is feeling a little down. It's definitely not confident enough to reject the null hypothesis. So, the answer is the null hypothesis looks believable.
To determine whether the null hypothesis looks believable or not, we need to compare the calculated test statistic (z) to the critical value.
In this case, the test statistic value is z = -0.98.
Since the test statistic is negative, we need to find the critical value for a one-tailed test at a 5% significance level (0.05).
Looking up the critical value from the z-table, we find it to be around -1.645.
Since the test statistic value is greater than the critical value (-0.98 > -1.645), we fail to reject the null hypothesis.
Therefore, the null hypothesis, that the population proportion p ≤ 0.3, looks believable.
Therefore, the correct answer to this question is: the null hypothesis looks believable.
To determine whether the alternative hypothesis or the null hypothesis looks believable, you need to compare the test statistic value to the critical value at the chosen significance level.
In this case, the null hypothesis is that the population proportion (p) is less than or equal to 0.3. The alternative hypothesis would be that p is greater than 0.3.
To make this comparison, you need to find the critical value at a 5% significance level. This critical value corresponds to the rejection region, which is the range of values that would lead you to reject the null hypothesis in favor of the alternative hypothesis.
Since the null hypothesis is written as p ≤ 0.3, the alternative hypothesis in this case would be p > 0.3.
To find the critical value for a one-tailed test at a 5% significance level, you can use a standard normal distribution table or a statistical software. For a one-tailed test, the critical value is z = 1.645.
Now, to determine whether the alternative or null hypothesis looks believable, compare the test statistic value with the critical value. If the test statistic value is greater than the critical value, it would suggest that the alternative hypothesis is believable. However, if the test statistic value is less than the critical value, it would suggest that the null hypothesis is believable.
In this case, the test statistic value is -0.98, which is less than the critical value of 1.645. Therefore, the null hypothesis looks believable, and we do not have enough evidence to reject it in favor of the alternative hypothesis.
So, the correct answer is: the null hypothesis looks believable.