Estimate the actual proportion of heads. Use a 95% confidence interval.

Estimate the actual proportion of heads. Use a 95% confidence interval.

Problem one

Someone flipped a coin 250 times and got heads 140 times. Let’s test a hypothesis about the fairness of this coin.

1. Estimate the actual proportion of heads. Use a 95% confidence interval.

SOLUTION

 Sample proportion

=0.56

Confidence level

Answer=0.4985/0.6215

1. Does your confidence interval provide evidence that the coin is unfair? Explain

Yes, the currency is unjust; this is because the confidence level is supposed to equal to 0.5, yet the standard is 0.05. The confidence is unfair also because the heads got is 140 higher than 125, which indicates a fair coin.

1. What is the significance level of this test? Explain

The significant degree of the test is 5%. Basing on our p values 0.4985 and 0.625, they are higher than the considerable level, therefore statistically insignificant.

Problem two

The AAP examined the parental influence on teenagers’ decisions to smoke. A group of students who never smoked was questioned about their parents’ attitudes toward smoking. These students were questioned again two years later to see if they had started smoking. The researchers found that, among the 284 students who indicated that their parents disapproved of kids smoking, 54 had become established smokers. Among the 41 students who initially said their parents were lenient about smoking, 11 became smokers.

1. Create a 95% confidence interval for the difference in the proportion of children who may smoke and have approving parents and those who may smoke and have disapproving parents.

SOLUTION

                =0.901

=0.2683

Confidence level

0.1431

0.1901-0.26880.1431

= -0.2213/0.0649

1.  Interpret your interval in this context.

  A confidence level of ninety-five percent indicates that the rate of smoking among the student whose parents disapprove ranges between -22.13% and 6.49% compared to those whose parents are lenient on smoking.

1. Explain what 95% confidence means.

The  confidence level means that the samples of the two population taken will have a 95% confidence interval reflecting a fair difference of the proportion selected from the population

Problem 3

A study examined the impact of depression on a patient’s ability to survive the cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for four years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among the patients who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones?

Write appropriate hypotheses.

SOLUTION

Symbol p1 represents people that died without depression while p2 died with depression.

Ho: p1-p2=0

Ha:p1-p20

Test your hypothesis and state your conclusion.

=0.1856

=0.2921

Proportion difference (0.1856-0.2921) =-0.1065

450(0.2921-018560

=0.47925

=-0.2222

The null hypothesis will be rejected because the proportion difference is low at-0.1065. The test indicates that cardiac disease affected by depression died more than the depressed.

Explain in this context what your P-value means.

The p-value indicates that there’s no more significant difference between the proportions.

If your conclusion is incorrect, which type of error did you commit?

The null hypothesis Ais incorrectly rejected, therefore a type one mistake.

Problem four

Researchers contacted more than 25,000 Americans aged 24 years to see if they had finished high school; 84.9% of the 12,460 males and 88.1% of the 12,678 females indicated that they had high school diplomas.

1. Create a 95% confidence interval for the difference in graduation rates between males and females.

SOLUTION 

Confidence level

84.9%*12460=10578.5

88.1%*12678=11169.3

=0.849

=0.881

=0.00844

(0.849-0.881)0.00844

-0.0236/-0.0404

1. Interpret your confidence interval.

A confidence level of 95% because the rat of males with high school diplomas is ranging between 2.36% and 4.04% lower than the female.

1. Does this provide strong evidence that girls are more likely than boys to complete high school? Explain.

There’s strong evidence because the confidence intervals contain only negative values, and the proportion difference is also a negative value, thus implying a higher rate of girl’s complete high school as compared to boys.

Find one aspect of this week’s material that is relevant to college, career, or everyday life. Provide some detail on how it could be significant.

Hypothesis testing is suitable as it helps in proper decision making and also the valuation of the significance of issues. The test helps in determining positive effects impacted on an area. The aspects help in finding solutions to questions and appraisal if a study is statistically significant.