Question

From a random sample of 587 items made by a particular manufacturing process, it is found that 19 are defective.

Test the research hypothesis that the proportion of defective items is different from 4%.

Copy and paste your R commands and output into your document.

(a) Using the correct notation, define the parameter of interest in this study. Then, state the null and alternative hypotheses.

(b) State the p-value.

(c) For your conclusion, give the level of evidence against H0 as very strong / strong / moderate / little to no evidence. Then, in a single plain English sentence, express the conclusion of this experiment in terms of the proportion of defective items being produced.

need help calculating this on R studio, thks

Answer 1

Given , in  the Question We have to use R studeo

We get to know ,it follows bin(n,p)

n = 587 , p(succeses) = 19/587 , lets assume  $\alpha$ = 0.05 because of not given in the Question

Vs $\ H_1: p \neq 0.04$

n <- 587
#no. of successes(defective) = 19
x <- 19
p <- 0.04
binom.test(x,n,p,conf.level = 0.95,alternative = 'two.sided')

#output of the above test becomes

Exact binomial test

data: x and n
number of successes = 19, number of trials = 587, p-value = 0.3993
alternative hypothesis: true probability of success is not equal to 0.04
95 percent confidence interval:
0.01959789 0.05008643
sample estimates:
probability of success
0.03236797

But this test is two sided ,So the probability of obtaining a more extreme value then the one actually obtain is   2* 0.3993 = 0.7986 which is greater that 0.05

Hence, We have very strongly insufficient evidance to reject Ho, at 5% level of significance

So , the proportion of defective items produced is 3.2% of the total items