The Correct option is Option A. Using hypothesis testing, The probability that Americans have changed their opinion on this issue since 2010 is 0.013.
Hypothesis testing:
Hypothesis testing is a form of statistical testing which uses data from a sample to determine population parameters or population probability distributions.
P stands for probability and measures the likelihood that each observed difference between groups is due to chance.
p-values are computed using the sampling distribution of the test statistic based on the null hypothesis, the sample data, and the type of test performed (bottom-tailed, top-tailed, or two-tailed).
The p-value for the lower tail test is given by: p-value = P(test statistic < observed test statistic | H 0 is true).
We have given that, In 2010 ,
americans favored mandatory testing of students in public schools as a way to rate the school = 73% = 0.73
In this year sample size= 1000
Sample proportion= 72% = 0.72
consider null hypothesis is true means there is a significant change in opinion of people's .
and alternative hypothesis implies there is no change in opinion of public .
Using the sample proportion in both year we see the test statistic value is greater than the observed test statistic value.
So, P -value is obtained about 0.013
and it gives null hypothesis can't be rejected.
Hence, the probability value 0.013 implies that a significant change in opinion of American public in this year since, 2010.
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Complete question :
In 2010 polls indicated that 73% of Americans favored mandatory testing of students in public schools as a way to rate the school. This year in a poll of 1,000 Americans 72% favor mandatory testing for this purpose. Has public opinion changed since 2010? We test the hypothesis that the percentage supporting mandatory testing is less than 73% this year. The p-value is 0.013.
Which of the following interpretation of this p-value is valid?
A) The probability that Americans have changed their opinion on this issue since 2010 is 0.013.
B) There is a 1.3% chance that the null hypothesis is true.
C) If 73% of Americans still favor mandatory testing this year, then there is a 1% chance that poll results will show 72% or fewer with this opinion .
