Respuesta :
Answer:
Given : In a random sample of 700 adults in that country, 33% say that they would travel into space on a commercial flight if they could afford it.
To find : (a) Identify the claim and state H0 and Ha.
(b) Use technology to find the P-value.
(c) Decide whether to reject or fail to reject the null hypothesis and (d) interpret the decision in the context of the original claim.
Solution:
A) Claim : A research center claims that 30% of adults in a certain country would travel into space on a commercial flight if they could afford it.
So, [tex]H_0:p=0.3\\H_a:p\neq0.3[/tex]
Now we are given that In a random sample of 700 adults in that country, 33% say that they would travel into space on a commercial flight if they could afford it.
n = 700
x = [tex]33\% \times 700 = \frac{33}{100} \times 700 = 231[/tex]
[tex]\widehat {p}=\frac{x}{n} =\frac{231}{700}=0.33[/tex]
We will use one sample proportion test .
Formula of test statistic =[tex]\frac{\widehat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
=[tex]\frac{0.33-0.3}{\sqrt{\frac{0.3(1-0.3)}{700}}}[/tex]
=[tex]1.73[/tex]
So, refer the z table for p value
B) p value = 0.9582
C) α = 0.10
p value > α
So, we accept the null hypothesis.
D) Hence we accept the claim that 30% of adults in a certain country would travel into space on a commercial flight if they could afford it.
