Question

A survey indicates that you should always try to negotiate for a better deal when shopping or paying for services. In fact, based on this survey, 32% of the people under the age of 34 were more likely to "haggle," compared to only 4% of those aged 65 and older. Suppose that this survey included 76 people under the age of 34 and 55 people who are 65 or older.

(a) What are the values of p̂under 34 and p̂65 or older for the two groups in this survey?

p̂under 34 =

p̂65 or over =

(b) Find a 95% confidence interval for the difference in the proportion of people who are more likely to "haggle" in the "under 34" versus "65 and older" age groups. (Round your answer to three decimal places.)

____________to___________

(c) What conclusions can you draw regarding the groups compared in part (b)?

Since the value punder 34 − p65 or older = 0 _________ (is/ is not) in the confidence interval, it is_________(likely the two portions are not the same/ possible two portions are the same) . You_________(should/ should not) conclude that there is a difference in the proportion of people who were more likely to "haggle" between the two groups. Since the probable values of punder 34 − p65 or older given by the interval contains__________(only negative/ only positive/ both positive and negative) numbers, the proportion of people under 34 who "haggle" is_______(possibly the same as/ likely greater than/ likely less than) the proportion of people 65 or older who "haggle".

Answer 1

(a) Proportion of prople under 34,   = 0.32

Proportion of prople 65 and over, = 0.04

(b) 95% confidence interval for the difference in the proportion of people who are more likely to "haggle" in the "under 34" versus "65 and older" age groups.

At = 0.05, the critical value, = 1.96

(c) Since the value = 0 is not in the confidence interval, it is likely the two portions are not the same. You should conclude that there is a difference in the proportion of people who were more likely to "haggle" between the two groups. Since the probable values of given by the interval contains only positive numbers, the proportion of people under 34 who "haggle" is likely greater than the proportion of people 65 or older who "haggle".