Please help I am having trouble with this problem please show all work and thank
ID: 3171551 • Letter: P
Question
Please help I am having trouble with this problem please show all work and thank you in advance!!! Ps part A is the picture below one study, based on responses tom 1024 that 39%of teenagers cite grades astheir greatestsourceof pressure use aoo5 significane level to testthe claim that fewer than half of a teenagers in the population feel that grades are their greatest source of pressure. Find the test statistic. z (Round to two decimal places as needed) Find the P-value for the found test statistics P-value L (Round to four decimal places as needed) State one conclusion Choose the correct answer below. Click to select your answerts)
Explanation / Answer
Solution:-
p = 0.39
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P > 0.50
Alternative hypothesis: P < 0.50
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the sample proportion is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.
Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).
= sqrt[ P * ( 1 - P ) / n ]
= 0.015625
z = (p - P) /
z = - 7.04
where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.
Since we have a one-tailed test, the P-value is the probability that the z-score is less than - 7.04. We use the Normal Distribution Calculator to find P(z < - 7.04) = less than 0.0001
Thus, the P-value = 0.00001
Interpret results. Since the P-value (0.0001) is less than the significance level (0.05), we cannot accept the null hypothesis.
From this we conclude that we have sufficient evidence in the favor of the claim that fewer than half of all teenagers in the population feel that grades are their greatest source of preesure.