A library is a collection of resources and books. Libraries often provide students the facilities to...

 

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A library is a collection of resources and books. Libraries often provide students the facilities to access electronic resources and the internet. Modem libraries are increasingly being redefined as places to get information in many formats and from many sources by providing material accessible by electronic means and a variety of digital tools. (a) Mr Raymond is a librarian at this library. He wishes to determine the proportions of students who use the library's electronic and digital resources this year. ) He surveyed 50 students and he found that 42 of them use these resources. Find Mr Raymond's 95% confidence interval for p, the proportions of students who use the library's electronic and digital resources this year. Interpret your answer. (2 marks) (i) Comment on the validity of the above confidence interval based on the Normality of the proportions. (2 marks) (iii) Mr. Raymond feels that his 95 % confidence interval above is too wide. He wants his new width to be 75 % of his original width. Determine the number of students he needs to survey in order to obtain this new width. (3 marks) (b) Mr Lee is another librarian at this library. He also wishes to detemine the proportions of students who use the library's electronic and digital resources this year. He surveyed 75 students and he found that 57 of them use these resources. Find Mr Lee's 95 % confidence interval and interpret it. (2 marks) (c) Mr Raymond believes that he is 95% confident that at least 73% of the students used the library's electronic and digital resources this year. Can Mr Lee's 95 % confidence interval support this belief? Explain your answer. (2 marks) (d) From the previous year's record, Mr Raymond leamt that 78 % of the students used the library's electronic and digital resources. Based on both the 95 % confidence intervals obtained by Mr Raymond and Mr Lee, comment on the reliability of the previous (2 marks) record. A library is a collection of resources and books. Libraries often provide students the facilities to access electronic resources and the internet. Modem libraries are increasingly being redefined as places to get information in many formats and from many sources by providing material accessible by electronic means and a variety of digital tools. (a) Mr Raymond is a librarian at this library. He wishes to determine the proportions of students who use the library's electronic and digital resources this year. ) He surveyed 50 students and he found that 42 of them use these resources. Find Mr Raymond's 95% confidence interval for p, the proportions of students who use the library's electronic and digital resources this year. Interpret your answer. (2 marks) (i) Comment on the validity of the above confidence interval based on the Normality of the proportions. (2 marks) (iii) Mr. Raymond feels that his 95 % confidence interval above is too wide. He wants his new width to be 75 % of his original width. Determine the number of students he needs to survey in order to obtain this new width. (3 marks) (b) Mr Lee is another librarian at this library. He also wishes to detemine the proportions of students who use the library's electronic and digital resources this year. He surveyed 75 students and he found that 57 of them use these resources. Find Mr Lee's 95 % confidence interval and interpret it. (2 marks) (c) Mr Raymond believes that he is 95% confident that at least 73% of the students used the library's electronic and digital resources this year. Can Mr Lee's 95 % confidence interval support this belief? Explain your answer. (2 marks) (d) From the previous year's record, Mr Raymond leamt that 78 % of the students used the library's electronic and digital resources. Based on both the 95 % confidence intervals obtained by Mr Raymond and Mr Lee, comment on the reliability of the previous (2 marks) record.

Answer rating: 100% (QA)

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