Question

A sample survey asked a random sample of 1498 adult Canadians, “Do you agree or disagree that all firearms should be registered?” Of the 1498 people in the sample, 1282 answered either “Agree strongly” or “Agree somewhat.” Assuming this survey can be considered an SRS of all adult Canadians, what is the proportion of all Canadians who agree (as described) that all firearms should be registered?

Your solution must include the following parts, in order. Point form is fine.

a) First answer each of these questions:

i) Does this call for a confidence interval or a hypothesis test?

ii) Is this 1 sample or 2 samples?

iii) Is this about mean(s) or proportion(s)?

iv) If this is about mean(s), do you know the SD of the population (σ — or σ1 & σ2 )? (If this is about proportions, skip this question.)

b) (1 pt) What are the population parameter(s), and what are the sample statistic(s)? Provide symbols, and say what they represent in the context of the question. (For example, "µ is the mean completion time of the population, and x̄ is the mean completion time for the sample".) You may want to give the statistic values here.

c) complete the question. Details depend on the kind of problem:

• For a confidence interval:

i) State the confidence level. (If it is not given, make a reasonable choice.)

ii) Give the formula for the margin of error (symbols only, no numbers!).

iii) Calculate the margin of error (show your work!).

iv) State the confidence interval in a complete sentence (in words!), in the context of the original problem. (You may use whichever form you prefer.)

• For a hypothesis test:

i) State the significance level (alpha). (If it is not given, make a reasonable choice.)

ii) Give the formula for the test statistic (z or t) (symbols only, no numbers!).

iii) State the null and alternative hypotheses. Use symbols, and state them in the context of the original problem. (A sketch is optional, but very useful.)

iv) Calculate the test statistic (z or t) (show your work!), and determine the p-value.

v) State your conclusion in a complete sentence (in words!), in the context of the original problem. Your conclusion should state whether or not you reject the null hypothesis, and what this says about the original question.

Answer 1

(a)

(i)

confidence interval

(ii)

1 sample

(iii)

proportion

(b)

= Population proportion

= Sample proportion

(c)

(i) Confidence level = 95% (Not given; reasonable choice)

(ii) Margin of Error (E) is given by:

(iii)

n = 1498

(iv) Confidence Interval:

0.8558 0.0091

= (0.8467 ,0.8649)

There is 95% probability that the Confidence Interval (0.8467 ,0.8649) will contain the true population proportion of all adult Canadians who agree that all firearms should be registered.