The batteries produced in a manufacturing plant have a mean time to failure of 30 months, with a standard deviation of 2 months.
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Answer:
a) With a confidence level of 98%, the percentage of all males who identify themselves as the primary grocery shopper are between 0.4962 and 0.5438.
b) The lower limit of the confidence interval is higher that 0.43, so if he conduct a hypothesis test, he will find that the data shows evidence to said that the fraction is higher than 43%.
c)
Step-by-step explanation:
If np' and n(1-p') are higher than 5, a confidence interval for the proportion is calculated as:
Where p' is the proportion of the sample, n is the size of the sample, p is the proportion of the population and is the z-value that let a probability of
on the right tail.
Then, a 98% confidence interval for the percentage of all males who identify themselves as the primary grocery shopper can be calculated replacing p' by 0.52, n by 2400, by 0.02 and
by 2.33
Where p' and are calculated as:
So, replacing the values we get:
With a confidence level of 98%, the percentage of all males who identify themselves as the primary grocery shopper are between 0.4962 and 0.5438.
The lower limit of the confidence interval is higher that 0.43, so if he conduct a hypothesis test, he will find that the data shows evidence to said that the fraction is higher than 43%.
Finally, the level of significance is the probability to reject the null hypothesis given that the null hypothesis is true. It is also the complement of the level of confidence. So, if we create a 98% confidence interval, the level of confidence is equal to 98%
It means the the level of significance is: