2 Data Management Questions

Hello I'm having difficulty solving the following two questions and I need your help!

(Step by step solutions would be very much appreciated if possible)

Use a significance level of 0.05 for each question.

Q1) A certain soft-drink manufacturer claims that its product holds 28% of the market. In a blind taste test, 13 out of 60 people chose this product. Does this test support or refute the soft drink manufacturer's claim? Choose a significance level you feel is appropriate for this situation.

Q2) An insurance company claims that 38% of automobile accidents occur within 5km of home. The company examined 400 recent accidents and found that 120 occurred within 5 km of the driver's home. Does this result support or refute the company's claim? Choose a significance level and justify your choice.

Re: 2 Data Management Questions

Both are hypothesis tests about proportions.

For Q1:

Ho: soft drink manufactured holds 28% of the market

Ha: soft drink does not hold 28% of the market (because they don't ask you to determine whether they hold more or less of that claim, it is a 2 tailed test).

your test static = z = (p'-p)/SQRT(pq/n)

where p' = sample proportion (for Q1, it would be 13/60)

p = Population proportion (for Q1, it would be 0.28)

q = 1 - p (1 - 0.288 = 0.712)

Your critical value

z, 0.05/2 (divide by 2 because it is a two tailed test)

= 1.960

we reject Ho if our C.V > T.S

we fail to reject Ho if our C.V < T.S

I'll let you substitute in for both questions, and see if you get the answer right.

If you have any problems just ask. You're best to set it out with:

1)hypotheses

2)distribution (call it hypothesis test about proportions in this case)

--> Include any assumptions; here it is n > or = 20, and both np and nq > or equal to 5.

3)critical value

4)find your test statistic

5)Action (do we reject or fail to reject Ho)

6)write conclusion in words.

(I'll do the calculation myself too)