Assume that a simple random sample has been selected from a normally distributed

Question

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.
A simple random sample of 25 filtered 100 mm cigarettes is obtained, and the tar content of each cigarette is measured. The sample has a mean of 18.8 mg and a standard deviation of 3.63 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg, which is the mean for unfiltered king size cigarettes. What do the results suggest, if anything, about the effectiveness of the filters?
a. test statistic=
b. pvalue =
c. State the final conclusion that addresses the original claim.
d. What do the results suggest, if anything, about the effectiveness of the filters?

2.

  
In a study of pregnant women and their ability to correctly predict the sex of their baby, 59 of the pregnant women had 12 years of education or less, and 39% of them correctly predicted the sex of their baby. Use a 0.05 significance level to test the claim that these women have no ability to predict the sex of their baby, and the results are not significantly different from those that would be expected with random guesses. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution.

a. test statistic=
b. pvalue=
c. Identify the conclusion about the null hypothesis and the final conclusion that addresses the original claim.

3.
1997, a survey of 900 households showed that 147 of them use e-mail. Use those sample results to test the claim that more than 15% of households use e-mail. Use a 0.05 significance level. Use this information to answer the following questions.
a. test statistic=
b. pvalue=
c. what is the conclusion?
d. Is the conclusion valid today? Why or why not?

4.
In a survey of 150 senior executives, 46.7% said that the most common job interview mistake is to have little or no knowledge of the company. Use a 0.01 significance level to test the claim that in the population of all senior executives, 40% say that the most common job interview mistake is to have little or no knowledge of the company. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution.
a. test statistic=
b. pvalue=
c. Identify the conclusion about the null hypothesis and the final conclusion that addresses the original claim.

Explanation / Answer

Given that,
population mean(u)=21.1
sample mean, x =18.8
standard deviation, s =3.63
number (n)=25
null, Ho: =21.1
alternate, H1: <21.1
level of significance, = 0.05
from standard normal table,left tailed t /2 =1.711
since our test is left-tailed
reject Ho, if to < -1.711
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =18.8-21.1/(3.63/sqrt(25))
to =-3.168
| to | =3.168
critical value
the value of |t | with n-1 = 24 d.f is 1.711
we got |to| =3.168 & | t | =1.711
make decision
hence value of | to | > | t | and here we reject Ho
p-value :left tail - Ha : ( p < -3.168 ) = 0.00207
hence value of p0.05 > 0.00207,here we reject Ho
ANSWERS
---------------
null, Ho: >21.1
alternate, H1: <21.1
test statistic: -3.168
critical value: -1.711
decision: reject Ho
p-value: 0.00207

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