Answer:
The p value for this case would be given by:
For this case the p value is higher than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion is not significantly different from 0.49 or 49%
Step-by-step explanation:
Information given
n=338 represent the random sample taken
X=148 represent the homes in Oregon were heated by natural gas
estimated proportion of homes in Oregon were heated by natural gas
is the value that we want to test
represent the significance level
z would represent the statistic
represent the p value
Hypothesis to test
We want to check if the true proportion of interest is 0.49, then the system of hypothesis are.:
Null hypothesis:
Alternative hypothesis:
The statitic is given by:
(1)
Replacing we got:
The p value for this case would be given by:
For this case the p value is higher than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion is not significantly different from 0.49 or 49%