1. Confidence Interval for a Population Proportion

1.a. The political affiliation of college freshmen is an important consideration to colleges and universities, political scientists, and political parties. In 2016, from a random sample of 500 college freshmen in the United States, 101 freshmen reported being conservatives. Calculate and interpret a 90% confidence interval for the proportion of college freshmen who label themselves as conservative.

Step 1. Verify that both random samples have at least 10 successes and 10 failures.

Step 2. Determine the critical value, Z , that corresponds to the chosen level of confidence.

Step 3. Compute the standard error & margin of error

Step 4. Compute the confidence interval point estimate margin of error = p E

Step 5. Interpret the confidence interval in context. We are ______% confident that the proportion of __________________________________ _____________________________________________ is between ____________ and __________.

1B: Hypothesis Test for a Population Proportion

The political affiliation of college freshmen is an important consideration to colleges and universities, political scientist, and political parties. In the year 2000, 18.9 % of college freshmen labeled themselves as Conservative and 24.8% of college freshmen labeled themselves as Liberal. In 2016, from a random sample of 500 college freshmen in the United States, 101 freshmen reported being conservative and 155 freshmen reported being liberal. We will use this sample to conduct a hypothesis test. Let's focus on the proportion of all U.S. college freshmen in 2016 who report being conservative . At the 5% significance level, does the sample above provide evidence that the proportion of U.S. college freshmen in 2016 who report being conservative is different than the proportion in 2000?

Step 1: Determine the Hypotheses

Define p in words: H 0 : p = H a : p Left tail, right tail or two tailed test?

Step 2: Collect the data Sample size, n= ________ Number of successes and failures ( Use p from H 0 ) ___________________ Random sampling? _________ Has the criteria for normality been met? ___________ Sample proportion (three decimals)p =____________________

Step 3: Assess the evidence Using p from H 0 , Mean = _______ _____________ ___________ P-value:________________

_Use normaldist( , ) Min______ Max________ =

Step 4: State a conclusion

Compare the p-value with the level of significance. What decisions should we make about the null and alternative hypotheses?

Explain what your decision means in the context of this problem.

1C:Hypothesis Test for Population Means

. For the past several years, the mean number of people in a household has been declining. A social scientist believes that in a certain large city, the mean number of people per household is less than 2.5. To investigate this, she takes a simple random sample of 150 households in the city, and finds that the sample mean number of people is 2.3 with a sample standard deviation of 1.5. Using a level of significance = 0.01 level. Can you conclude that the mean number of people per household is less than 2.5?

Step 1: Determine the hypotheses

Define in words

H 0 :

H a :

Step 2: Collect the data

Sample size =_______ Sample mean =__________ Sample standard deviation __________ Random sampling? __________ Criteria for approximate normality met? __________

Step 3: Assess the evidence

Test statistic : _____________

P-value=__________ Use desmos tdist (d.f.=______) , min _________, max__________

Step 4: State a conclusion

Compare the p-value with the level of significance . What decisions should we make about H 0 and H a?

Explain what your decision means in the context of this problem.

1D :Hypothesis Test for Paired Data

An accounting firm tested two spreadsheet applications to determine whether there is a difference between them in the mean speed with which a standard accounting problem can be solved. The times needed for each of twelve accountants to solve the problem are included in the table below. Can you conclude that the mean me differs between the two applications? Use the = 0.05 level of significance. Assume that a simple random sample has been selected from a normally distributed population and test the given claim.

Application 1 2 3 4 5 6 7 8 9 10

a 42 34 45 35 40 44 48 49 41 33

a 42 34 45 35 40 44 48 49 41 33

d= a-b_____________________________

Step 1: Determine the hypotheses Define in words: "The mean difference ...... H 0 : (assuming there is no difference) H a : (use <, > or =/ depending on the claim) Significance level = Right-tailed, Left-tailed or Two-tailed Test?

Step 2: Collect the data Random sampling? Normality? n >30 OR that sample comes from a normal population.

n = number of paired differences in the sample =

x = mean(d) is the mean of the sample differences =

s= stdev(d) is the sample standard deviation of sample differences =

Step 3: Assess the evidence ______________ P-value=__________ Use desmos tdist(df) to find the p-value

Step 4: State a conclusion Compare the p-value with the level of significance. What decisions should we make about H 0 and H a?

Explain what your decision means in the context of this problem 5.3 Confidence Intervals for Two Population Proportion.

1E:Confidence Intervals for Two Population Proportions

In August and September 2005, Hurricanes Katrina and Rita caused extraordinary flooding in New Orleans, Louisiana. Many homes were severely damaged or destroyed, and of those that survived, many required extensive cleaning. It was thought that cleaning flood-damaged homes might present a health hazard due to the large amounts of mold present in many of the homes. In a sample of 365 residents of Orleans Parish who had precipitated in the cleaning of one or more homes, 77 had experienced symptoms of wheezing, and in a sample of 179 residents who had not precipitated in cleaning, 23 reported wheezing symptoms.

Calculate and interpret a 99% confidence interval for the difference in the proportion of residents with wheezing symptoms among those who precipitated in the cleaning of flood-damaged homes and those who did not. Let population 1 represent those who precipitated in the cleaning of one or more homes and population 2 those who did not precipitate in cleaning. Step

1. Verify that both random samples have at least 10 successes and 10 failures.

Step 2. Determine the critical value, Zc , that corresponds to the chosen level of confidence.

Step 3. Compute the margin of error:

Step 4. Compute the confidence interval Statistic Margin of Error

Step 5. Interpret the confidence interval in context. We are ______% confident that the difference between the __________________________________ _____________________________________________ is between ____________ and __________. Furthermore, since the confidence interval [pick one: contains zero/is positive/is negative], we conclude that ____________________________________________________________________.

1F :Hypothesis Testing for Two Population Proportions

A sample of 200 voters over the age of 60 were asked whether they thought Social Security benefits should be increased for people over the age of 65. A total of 95 of them answered yes. A sample of 150 voters aged 18-25 were asked the same queson and 63 of them answered yes. A pollster wants to know whether the proportion of voters who support an increase in Social Security benefits is greater among older voters. He will use the = 0.05 level of significance.

Step 1: Determine the Hypothesis

Define the population proportions p1 and p2 in words

p1

p2

H 0 :

H a : Type of tail test:

Step 2: Collect the Data Normality Criteria Met?

n 1= , x 1 , p 1 = x1 /n1 = n2 = , x2 = , p2 = x2/ n2 =

Step 3: Assess the Evidence Do the calculations one step at a me and round intermediate steps to three decimal places. Pooled Proportion = p

Estimated standard error = Test Statistic: Z = p1- p 2 /standard error

P-value _________ Use desmos normaldist(0,1)

Step 4: State the Conclusion Compare the p-value with level of significance . What decisions should we make about H 0 and H a ?

Explain what your decision means in the context of this problem.