Question

A Poll of 958 of all national registered voters found that, in the first week of June 2020, asked the question “how much confidence do you have in police officers in your community to treat black people and white people equally: a great deal of confidence, a fair amount, just some, or very little confidence?”. Some results of the poll are as follows:

• There were 604 white respondents, and 70% of the white respondents responded that they had “a great deal, or a fair amount” of confidence.

• There were 354 non-white respondents, and 50% of the non-white respondents responded that they had “a great deal, or a fair amount” of confidence.

1. Use the 2SD method to find a 95% confidence interval estimate of the percentage of all white national registered voters who feel that they have “a great deal, or a fair amount” of confidence that the police officers in their community treat black people and white people equally. Show all the work to use the 2SD method to find the confidence interval.
2. Use the applet to find a 95% confidence interval estimate of the percentage of all non-white national registered voters who feel that they have “a great deal, or a fair amount” of confidence that the police officers in their community treat black people and white people equally.
3. According to the results above, is it plausible that a majority (i.e. more than 50%) of all nationally registered WHITE voters have “a great deal, or a fair amount” of confidence that the police officers in their community treat black people and white people equally? EXPLAIN your reasoning for your conclusion.
4. According to the results above, is it plausible that a majority (i.e. more than 50%) of all nationally registered NON-WHITE voters have “a great deal, or a fair amount” of confidence that the police officers in their community treat black people and white people equally? EXPLAIN your reasoning for your conclusion.

Answer 1

a)

95%   Confidence Interval is              
Interval Lower Limit = p̂ - E =    0.70000   -   0.03655   =   0.6635
Interval Upper Limit = p̂ + E =   0.70000   +   0.03655   =   0.7365

b)

Level of Significance,   α =    0.05          
  
Sample Size,   n =    354          
                  
Sample Proportion ,    p̂ = x/n =    0.5000          
z -value =   Zα/2 =    1.960   [excel formula =NORMSINV(α/2)]      
                  
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.026575          
margin of error , E = Z*SE =    1.960   *   0.02657   =   0.0521
                  
95%   Confidence Interval is              
Interval Lower Limit = p̂ - E =    0.50000   -   0.05209   =   0.4479
Interval Upper Limit = p̂ + E =   0.50000   +   0.05209   =   0.5521
                  
95%   confidence interval is (   0.448   < p <    0.552   )

c)

YES

Because the interval does not contain the value the 50%

d)

NO

Because the interval does contain the value the 50%

Please let me know in case of any doubt.

Thanks in advance!

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