Question

- 9 of 13 ID: MST.HT.TP.01.0060 [1 point] A confidence interval is constructed for an unknown population proportion, p. A sample is collected, and the 95% confidence interval is calculated to be 0.43 + 0.05. Based on this information, it is most accurate to say that there is approximately 95% confidence in the assertion that: the population proportion is between 0.38 and 0.48 the sample proportion is between 0.38 and 0.48 the population proportion is 0.43 O the sample proportion is 0.43 - 10 of 13 ID: MST.HT.TP.01.0040 [1 point] Three years ago, a referendum was held to decide on whether to pass Proposition 4815162342. Every eligible voter in the nation voted on this proposition, and it was denied. The proportion of 'yes' votes was p = 0.4. Since that day, the government has released a variety of public service announcements in favour of the proposition. Today, the government believes that the proportion of 'yes' votes has increased from its figure three years ago. A hypothesis test is conducted to test this. Select the correct null and alternative hypotheses: O Ho: p = 0.4 Ha: p = 0.4 o Ho: p = 0.4 Ha: p > 0.4 O Ho:p # 0.4 Ha: p = 0.4 о Ho: p < 0.4 Hai p > 0.4 O Ho: p > 0.4 Ha: p = 0.4 о Ho: p = 0.4 Ha: p < 0.4 - 11 of 13 ID: MST.CI.CIP.04.0020 [3 points] You have been given the task of finding out what proportion of students that enroll in a local university actually complete their degree. You have access to first year enrolment records and you decide to randomly sample 116 of those records. You find that 82 of those sampled went on to complete their degree. a) Calculate the proportion of sampled students that complete their degree. Give your answer as a decimal to 3 decimal places. Sample proportion = You decide to construct a 95% confidence interval for the proportion of all enrolling students at the university that complete their degree. If you use your answer to part a) in the following calculations, use the rounded version. b) Calculate the lower bound for the confidence interval. Give your answer as a decimal to 3 decimal places. Lower bound for confidence interval = c) Calculate the upper bound for the confidence interval. Give your answer as a decimal to 3 decimal places. Upper bound for confidence interval =

Answer 1

9)

the population proportion is between 0.38 and 0.48

........

10)

Ho: p = 0.4 Ha: p > 0.4

..........

11)

a)

Number of Items of Interest,   x =   82
Sample Size,   n =    116
      
Sample Proportion ,    p̂ = x/n =    0.707

..........

b)

z -value =   Zα/2 =    1.960   [excel formula =NORMSINV(α/2)]      
                  
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.042263          
margin of error , E = Z*SE =    1.960   *   0.04226   =   0.0828
                  

Interval Lower Limit = p̂ - E =    0.70690   -   0.08283   =   0.624

c)

Interval Upper Limit = p̂ + E =   0.70690   +   0.08283   =   0.790
                  
.............

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