Question

*A cereal company claims that 38% of their boxes of cereal have prizes inside. You buy a total of 20 boxes and find that 6 of the boxes had prizes in them. Test the hypothesis that the true proportion of boxes of cereal with prizes inside is different from 38%. Use an alpha level of .05*

```{r}
?t.test
```

Please make sure you solve in R-studio. Solving without giving me R-codes will not help me. It would also help if you write a brief explanation of what you did. Thanks in advance!

Answer 1

Sol:

Its a ztets from proportion:

Rcode:

Ztest_Prop = function(x,n,p) {
p_hat = x/n
diff=p_hat-p
se =sqrt(p*(1-p)/n)
zstat=diff/se
zstat1=abs(zstat)
pval = 2*pnorm(zstat1, lower.tail=FALSE)
c(Teststatistic=zstat,Pvalue=pval)
}
Ztest_Prop(6,20,p=0.38)

Output:

Teststatistic Pvalue
-0.73708 0.46107

ANSWER:

Ho:p=0.38

Ha:p not =0.38

alpha=0.05

z= -0.73708

p=0.46107

p>0.05

Fail to reject Ho

Accept Ho

There is no suffcient evidence at 5% level of significance to conlcude that

the true proportion of boxes of cereal with prizes inside is different from 38%.

Answer 2

Modern English is analytic (i.e., relatively uninflected), whereas Proto-Indo-European, the ancestral tongue of most of the modern European languages (e.g., German, French, Russian, Greek), was synthetic, or inflected. During the course of thousands of years, English words have been slowly simplified from the inflected variable forms found in Sanskrit, Greek, Latin, Russian, and German, toward invariable forms, as in Chinese and Vietnamese. The German and Chinese words for the noun man are exemplary. German has five forms: Mann, Mannes, Manne, Männer, Männern. Chinese has one form: ren. English stands in between, with four forms: man, man’s, men, men’s. In English, only nouns, pronouns (as in he, him, his), adjectives (as in big, bigger, biggest), and verbs are inflected. English is the only European language to employ uninflected adjectives; e.g., the tall man, the tall woman, compared to Spanish el hombre alto and la mujer alta. As for verbs, if the Modern English word ride is compared with the corresponding words in Old English and Modern German, it will be found that English now has only 5 forms (ride, rides, rode, riding, ridden), whereas Old English ridan had 13, and Modern German reiten has 16.