Question

"Japanese Girls’ Names"

by Kumi Furuichi

It used to be very typical for Japanese girls’ names to end with “ko.” (The trend might have started around my

grandmothers’ generation and its peak might have been around my mother’s generation.) “Ko” means “child” in Chinese characters. Parents would name their daughters with “ko” attaching to other Chinese characters which have meanings that they want their daughters to become, such as Sachiko—happy child, Yoshiko—a good child, Yasuko—a 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 “ko.” 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’s generation would have names with “ko” at the end,

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

acquaintances’ 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.

Short answer

Confidence Interval: (0.453, 0.658)

Step-by-step solution

Find H0 and Ha: We want to test if Japanese girls students take less than 70% of the friends and acquaintances having names start with 'Ko', on average.

$H_0:p\ge 0.70;H_a:p<0.70$

Determine the distribution needed:In words, CLEARLY state what your random variable P′ represents.P′ = The proportion of friends or acquaintances who have a name ending in “ko.”

Normal: $N\left(0.7,\sqrt{\frac{(0.7)(1-0.7)}{80}}\right)$

Test Statistic:$z=-2.99$

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

$p-value=0.0014$

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

If the null hypothesis is true (the proportion is 0.70), then there is a 0.0014 probability that the sample (estimated) proportion is 0.4375 or more.

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.

alpha	decision	reason for decision
0.01	Do not reject H0	$\alpha <p-value$

Conclusion: At the 1% significance level, there is sufficient evidence to conclude that the proportion of friends or acquaintances who have a name ending in “ko” is less than 0.70.

Confidence Interval

Confidence Interval: (0.453, 0.658): The “plus-4s” confidence interval is (0.453, 0.654).