Reference no: EM132361795

Question

In the survey completed by students at the start of this year one question asked was gender (male/female), and another question asked was hemisphere of birth (northern/southern).

60% of respondents were female.

28% of respondents were born in the northern hemisphere.

45% of respondents were female and born in the southern hemisphere.

i) Show that the percentage of respondents who were male and born in the northern hemisphere is 13%.

ii) A student is chosen at random from those who responded to the survey. Let N be the event the student was born in the northern hemisphere and M be the event the student is male.

a) What is the probability that the student was born in the northern hemisphere? That is, compute P(N).

b) Suppose the chosen student is known to be male. What is the con- ditional probability that the student was born in the northern hemi- sphere, given that the student is male? That is, compute P(NIM).

c) Are the events the student is male and the student was born in the northern hemisphere independent? Use the definition of indepen- dence given in and give reasons for your answer.

(iii) Another survey question asked about transport to school (bicycle, bus, car, car/train/bus, motorbike, train/bus, walking, other). There were 400 students who responded to the survey and 61 students indicated that they walk to school.

a) What proportion of the respondents indicated that they walk to school?

b) Assume that the 400 students who responded to the survey can be considered as a random sample of school students from the point of view of method of travel to school. Using the normal approximation to the sample proportion, determine an approximate 90% confidence interval for the proportion of school students who walk to school.

c) For the confidence interval computed for part b), you were asked to assume that the 400 students who responded to the survey can be considered as a random sample of school students from the point of view of method of travel to school. Do you think that this is a reasonable assumption? Give a reason for your answer.