N = 1,166 pet owners

Margin of Error ( 2.9)

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.

"Overall, do you like, dislike or neither like nor dislike dogs? . . . A lot or a little?"

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Like a Lot

Pet owners

84%

1.Calculate confidence interval estimates for the proportion

a.State the confidence interval using the MoE. What does this confidence interval estimate?

i.Like a lot: (84-2.9%, 84+2.9%) = (81.1%-86.9%)

b.Use the Confidence Interval template (found in this module'sLiveBinder) to calculate the confidence interval based on the sample size and the number of successes (the proportion you are interested in). Use a confidence level of 95%.

Confidence Interval for Proportion (Number of Success Unknown)

Sample Size

1166

Confidence Level

95.00%

Proportion of sample

84.00%

z - score for the left side of the confidence interval

-1.95996

z - score for the right side of the confidence interval

1.95996

Standard Error of the proportion

0.01074

Lower Limit = proportion - standard error*z -score

0.81896

Upper Limit = proportion + standard error*z -score right side

0.86104

c.What is the calculated confidence interval?

i.Confidence interval is (0.81896-0.86104) or (81.896%-86.104%)

ii.The confidence interval based on number of successes is 0.796 higher and lower than the interval based on the sample size.The margin is smaller.

2.Compute sample size needed for the confidence interval of the proportion.

a.Calculate the sample size needed for the given margin of error and see if the poll had enough people surveyed. Use the sample size template (found in this module'sLiveBinder) to find the sample size needed.

Sample Size for Proportion

Estimate of True Proportion

0.84

Sampling Error

0.029

Confidence Level

95.00%

Z Score

-1.95996

Calculated Sample Size

614

The sample size needed is 614.They had enough samples.

3.Describe hypothesis testing to test a population proportion

a.Suppose that you do not believe that the poll is accurate.You are to make a hypothesis test to determine the validity of the poll testing its proportion.

i.I feel the proportion should be greater than the proportion 0.84.

ii.The null hypothesis is the proportion for the number of people who think dogs are amazing is 84%.

iii.The alternative hypothesis is the proportion for the number of people who think dogs are amazing is greater than 84%.

iv.The level of significance I am choosing is 0.05.

4.Testing a Hypothesis about a Population proportion.

a.Suppose that you conduct a study on your situation in which the sample statistic produces a test statistic of 2.13.

i.0.05 corresponds to a z-score of 1.64, compared to a test static of 2.13, I should reject the null hypothesis. I should reject the null hypothesis because the significance value is below the set value.

ii.I would need to fail to reject the null hypothesis, meaning the test statistic would need to be greater than or equal to 2.13.This means a p-value of 1 which means the level of significance would have to be less than 0.0165.For example: 0.011 is less than 0.0165 versus 0.05.This is because the level of significance is higher meaning I fail to reject the null hypothesis and accept the alternative hypothesis.

Can you please help me understand what is incorrect on this?