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Chapter 9: Q.100 (page 553)

According to an article in Bloomberg Businessweek, New York City's most recent adult smoking rate is 14%. Suppose that a survey is conducted to determine this year鈥檚 rate. Nine out of 70 randomly chosen N.Y. City residents reply that they smoke. Conduct a hypothesis test to determine if the rate is still 14% or if it has decreased.

Short Answer

Expert verified

Confidence Interval: (0.0502, 0.2070)

Step by step solution

01

Find H0 and Ha: We want to test if New York City (NYC) adults take less than 14% of them to smoke, on average.

H0:p=0.14;Ha:p<0.14

02

Determine the distribution needed: In words, CLEARLY state what your random variable P′ represents.Let P′ = the proportion of NYC residents that smoke.

Normal:N0.14,(0.14)(1-0.14)70

Test Statistic:z=鈥�0.2756

03

Calculate the p-value using the normal distribution for proportions:

p-value=0.3914

In one to two complete sentences, explain what the p-value means for this problem.

If the null hypothesis is true (the proportion is 0.14), then there is a 0.3914 probability that the sample (estimated) proportion is 0.129 or more.

04

Compare α and the p-value:Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion, using complete sentences.

alphadecisionreason for decision
0.05Do not reject the null hypothesis.
p-value>0.05

Conclusion: At the 5% significance level, there is insufficient evidence to conclude that the proportion of NYC residents who smoke is less than 0.14.

05

Confidence Interval

Confidence Interval: (0.0502, 0.2070): The 鈥減lus-4s鈥� confidence interval (see chapter 8) is (0.0676, 0.2297).

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Most popular questions from this chapter

The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5a percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100people in a certain town, seven of them suffered from depression or a depressive illness. If you were conducting a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population, what would the null and alternative hypotheses be?

localid="1650439913140" a.H0__________

b.Ha __________

Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization

thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they

spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test.

The null and alternative hypotheses are:

a.Ho:x炉=4.5,Ha:x炉>4.5b.Ho:渭鈮�4.5,Ha:渭<4.5c.Ho:渭=4.75,Ha:渭>4.75d.Ho:渭=4.5,Ha:渭>4.5

H0: 渭 = 10, Ha: 渭 < 10 Assume the p-value is 0.0935. What type of test is this? Draw the picture of the p-value.

From generation to generation, the mean age when smokers first start to smoke varies. However , the standard deviation pf that age remains constant of around 2.1years . A survey of 40smokers of this generation was done to see if the mean starting age is at least 19. the sample mean was 18.1 with a sample standard deviation of1.3do the data support the claim at the 5%level?

"Japanese Girls鈥� Names"

by Kumi Furuichi

It used to be very typical for Japanese girls鈥� names to end with 鈥渒o.鈥� (The trend might have started around my

grandmothers鈥� generation and its peak might have been around my mother鈥檚 generation.) 鈥淜o鈥� means 鈥渃hild鈥� in Chinese characters. Parents would name their daughters with 鈥渒o鈥� attaching to other Chinese characters which have meanings that they want their daughters to become, such as Sachiko鈥攈appy child, Yoshiko鈥攁 good child, Yasuko鈥攁 healthy child, and so on.

However, I noticed recently that only two out of nine of my Japanese girlfriends at this school have names which end with 鈥渒o.鈥� More and more, parents seem to have become creative, modernized, and, sometimes, westernized in naming their children.

I have a feeling that, while 70 percent or more of my mother鈥檚 generation would have names with 鈥渒o鈥� at the end,

the proportion has dropped among my peers. I wrote down all my Japanese friends鈥�, ex-classmates鈥�, co-workers, and

acquaintances鈥� names that I could remember. Following are the names. (Some are repeats.) Test to see if the proportion has

dropped for this generation.

Ai, Akemi, Akiko, Ayumi, Chiaki, Chie, Eiko, Eri, Eriko, Fumiko, Harumi, Hitomi, Hiroko, Hiroko, Hidemi, Hisako,

Hinako, Izumi, Izumi, Junko, Junko, Kana, Kanako, Kanayo, Kayo, Kayoko, Kazumi, Keiko, Keiko, Kei, Kumi, Kumiko,

Kyoko, Kyoko, Madoka, Maho, Mai, Maiko, Maki, Miki, Miki, Mikiko, Mina, Minako, Miyako, Momoko, Nana, Naoko,

Naoko, Naoko, Noriko, Rieko, Rika, Rika, Rumiko, Rei, Reiko, Reiko, Sachiko, Sachiko, Sachiyo, Saki, Sayaka, Sayoko,

Sayuri, Seiko, Shiho, Shizuka, Sumiko, Takako, Takako, Tomoe, Tomoe, Tomoko, Touko, Yasuko, Yasuko, Yasuyo, Yoko, Yoko, Yoko, Yoshiko, Yoshiko, Yoshiko, Yuka, Yuki, Yuki, Yukiko, Yuko, Yuko.
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