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Manelli Perfume Company recently developed a new fragrance that it plans to market under the name Heavenly. A number of market studies indicate that Heavenly has very good market potential. The sales department at Manelli is particularly interested in whether there is a difference in the proportions of younger and older women who would purchase Heavenly if it were marketed at a 5% significance level. There are two independent populations, a population consisting of the younger women and a population consisting of the older women. Each sampled woman was asked to smell Heavenly and indicate whether she likes the fragrance well enough to purchase a bottle. The random sample of 120 young women revealed that 23 liked the Heavenly fragrance well enough to purchase it. Similarly, a sample of 225 older women revealed that 70 liked the fragrance well enough to make a purchase.

          Manelli Perfume Company recently developed a new fragrance that it plans to market under the name Heavenly. A number of market studies indicate that Heavenly has very good market potential. The sales department at Manelli is particularly interested in whether there is a difference in the proportions of younger and older women who would purchase Heavenly if it were marketed at a 5% significance level. There are two independent populations, a population consisting of the younger women and a population consisting of the older women. Each sampled woman was asked to smell Heavenly and indicate whether she likes the fragrance well enough to purchase a bottle. The random sample of 120 young women revealed that 23 liked the Heavenly fragrance well enough to purchase it. Similarly, a sample of 225 older women revealed that 70 liked the fragrance well enough to make a purchase.
        
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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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Manelli Perfume Company recently developed a new fragrance that it plans to market under the name Heavenly. A number of market studies indicate that Heavenly has very good market potential. The sales department at Manelli is particularly interested in whether there is a difference in the proportions of younger and older women who would purchase Heavenly if it were marketed at a 5% significance level. There are two independent populations, a population consisting of the younger women and a population consisting of the older women. Each sampled woman was asked to smell Heavenly and indicate whether she likes the fragrance well enough to purchase a bottle. The random sample of 120 young women revealed that 23 liked the Heavenly fragrance well enough to purchase it. Similarly, a sample of 225 older women revealed that 70 liked the fragrance well enough to make a purchase.
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Transcript

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00:01 Hello, let's have a look on the question.
00:02 Two samples that are given to us.
00:03 Here, n1 is equal to 120 and x1 is equal to 23.
00:09 Next we have n2 is equal to 225 and x2 is equal to 70.
00:15 Now we need to find out the proportions.
00:18 Proportion p1 is equal to x1 by n1 which is equal to 0 .192.
00:24 And proportion for p2, x2 by n2 that is 0 .31.
00:32 Now p will be equal to x1 plus x2 divided by n1 plus n2 which is equal to 0 .2696.
00:43 Now we have all the values.
00:45 Now we need to define none and alternating hypothesis.
00:47 So none hypothesis h0 and alternative hypothesis h1...
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