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The mean age of De Anza College students in a previous term was 26.6 years old. An instructor thinks the mean age for online students is older than 26.6. She randomly surveys 56 online students and finds that the sample mean is 29.4 with a standard deviation of 2.1. Conduct a hypothesis test.

Short Answer

Expert verified

CI:(28.8, 30.0)

Step by step solution

01

Find H0 and Ha: We want to test if De Anza College students take less than 26.6 years old mean age for them while conducting online classes, on average.

H0:=26.6;Ha:>26.6

02

Determine the distribution needed: In words, CLEARLY state what your random variable x represents.Let x = the mean age for online students at De Anza College.

Normal: N26.6,2.156

Test statistic:z=9.98

03

Calculate the p-value using the normal distribution for mean RV

p-value=0.0000

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

If the null hypothesis is true (the mean age is 26.6), then there is a 0.0000 probability that the sample (estimated) mean age is 29.4 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
0.01Reject the null hypothesis.
p-value<0.01

Conclusion: There is sufficient evidence to conclude that the mean age of online students at De Anza College is greater than 26.6 years.

05

Confidence Interval

CI: (28.8, 30.0)

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The US Department of Energy reported that 51.7% of homes were heated by natural gas. A random sample of 221homes in Kentucky found that 115 were heated by natural gas. Does the evidence support the claim for Kentucky at the =0.05 level in Kentucky? Are the results applicable across the country? Why?

"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.

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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,

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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.

A normal distribution has a standard deviation of 1.We want to verify a claim that the mean is greater than12.

A sample of 36is taken with a sample mean of12.5.

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It is believed that Lake Tahoe Community College (LTCC) Intermediate Algebra students get less than seven hours of sleep per night, on average. A survey of 22 LTCC Intermediate Algebra students generated a mean of 7.24 hours with a standard deviation of 1.93 hours. At a level of significance of 5%, do LTCC Intermediate Algebra students get less than

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