A sample survey funded by the National Science Foundation asked a random sample of American adults about biological evolution. One question asked survey participants to answer "True", "False" or "Not sure" to the statement "Human beings, as we know them today, developed from earlier species of animals." Of the 384 respondents, 165 said "True". Is there sufficient evidence to conclude that fewer than half of American adults think that humans developed from earlier species of animals? Use a 5% level of significance.
Part A. Test of Significance
STATE:
At the α = 0.05 level, is there sufficient evidence to conclude that fewer than half of American adults think that humans developed from earlier species of animals? (Write this verbatim on your paper.)
Answer all of the following questions in complete sentences when applicable.
PLAN:
(1) State the name of the appropriate test procedure you will use (e.g., one-sample t test for means). (1 pt)
(2) Describe the parameter of interest in the context of the problem. (1 pt)
(3) State the null and alternative hypotheses. (2 pts)
(4) Write down the significance level. (1 pt.)
SOLVE:
(5) List and check the conditions for the test procedure you named above. (4 pts)
(6) Obtain the value of the sample proportion. (1 pt)
(7) Write the calculated test statistic (including your calculations) and its associated P-value using the appropriate table, not from statistical software. (2 pts)
CONCLUDE:
(8) Answer the question posed in the STATE step in context. Do this by including these three parts in your conclusion (3 pts):
- Compare P-value with α
- Decide whether to reject or fail to reject the null hypothesis
- State your conclusion in context
Part B. Confidence Interval Estimation
STATE:
What is a 90% confidence interval estimate for the proportion of all American adults who think that humans developed from earlier species of animals? (Please write this verbatim on your paper)
PLAN:
(1) State the name of the appropriate estimation procedure (e.g. one-sample t confidence interval for estimating the mean difference). (1 pt)
(Note) You have already described the parameter being estimated in part A, so you don't have to repeat it here.
SOLVE:
(1) You have already listed the conditions, now check the condition for the normality of the sampling distribution of p-hat for confidence interval estimation. (1 pt.)
(2) Write down the confidence level and the z* critical value. (2 pts.)
(3) Calculate the confidence interval in interval form. Be sure to show your work. (2 pts)
CONCLUDE:
(4) Interpret your confidence interval in context. Do this by including these three parts in your conclusion (3 pts):
- Level of confidence
- Parameter of interest in context
• The interval estimate