Question

All euro (common currency in Europe) coins have a national image on the “heads” side and a common design on the“tails” side. Spinning a coin, unlike tossing it, may not give heads and tails equal probabilities. Polish students spun the Belgian euro 280 times, with its portly king, Albert, displayed on the heads side. The result was 153 heads. At a 10% significance level, does this demonstrate that the chances of "heads" when spinning a Belgian euro are different from tossing it?

a) 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) 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) (3 pts) 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)Does this call for a confidence interval or a hypothesis test?

This is hypothesis test. We are asked to test at a 10% significance level, does this demonstrate that the chances of "heads" when spinning a Belgian euro are different from tossing it?

ii) Is this 1 sample or 2 samples?

1 Sample.

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

Its Proportion.

sample size is 280 so n= 280 and sample proportion will be p = 153/280 =0.55

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.)

This is proportion.

Please post remaining questions separately. Thanks and God Bless You :)

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