Respuesta :
Answer:
The decision is to fail to reject the Null Hypothesis. The conclusion is that there is not enough evidence to support the claim.
Step-by-step explanation:
A one-proportion z-test can be used to determine whether the proportion of cars with manual transmission is less than 10%.
The hypothesis is defined as:
H₀: The proportion of cars with manual transmission is 10%, i.e. p = 0.10.
Hₐ: The proportion of cars with manual transmission is less than 10%, i.e. p < 0.10.
The information provided is:
[tex]X=95\\n=1000\\\alpha =0.05\\p-value=0.299[/tex]
The test statistic is:
[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
Decision rule:
If the p-value of the test is less than the significance level (α) then the null hypothesis will be rejected or else accepted.
The p-value = 0.299 > α = 0.05.
The null hypothesis was failed to rejected at 5% level of significance.
Conclusion:
As the null hypothesis was not rejected it can be concluded that the proportion of cars with manual transmission is 10%.
Thus, the correct option is:
"The decision is to fail to reject the Null Hypothesis. The conclusion is that there is not enough evidence to support the claim."
Answer:
The calculated value Z = 22.22 > 1.96 at 5% level of significance
Therefore the null hypothesis is rejected.
The conclusion is that there is not enough evidence to support the claim
Step-by-step explanation:
Step 1:-
A researcher claims that the proportion of cars with manual transmission is less than 10%.
P = 10% = 0.10
Given sample size n= 1000
given the Sample proportion is p = 0.299
Null hypothesis: H₀: P =0.10
Alternative hypothesis :Ha:p<0.10
Level of significance α=0.05
Step 2:-
The test of hypothesis [tex]Z = \frac{p-P}{\sqrt{\frac{PQ}{n } } }[/tex]
put all values , we get
[tex]Z = \frac{0.299-0.10}{\sqrt{\frac{0.10X0.90}{1000 } } }[/tex]
on calculation , we get
[tex]Z = \frac{0.199}{0.0094} = 22.22[/tex]
The 5 % level of significance of tabulated value = 1.96
Conclusion:-
The calculated value Z = 22.22 > 1.96 at 5% level of significance
Therefore the null hypothesis is rejected.
The conclusion is that there is not enough evidence to support the claim
