Answer :
Null hypothesis (Hₒ): The standard deviation of electric bulbs manufactured by BIG Corporation is greater than or equal to 122 days.
Alternative hypothesis (H₁): The standard deviation of electric bulbs manufactured by BIG Corporation is less than 122 days.
To conduct the hypothesis test, we need to calculate the test statistic based on the given information. Since we are dealing with the standard deviation, we'll use a chi-square test statistic.
The formula for the chi-square test statistic for testing the population standard deviation when the population mean is known is:
[tex]\[ \chi^2 = \frac{(n-1)s^2}{\sigma^2} \][/tex]
Where:
-n is the sample size
-s is the sample standard deviation
- [tex]\( \sigma \)[/tex] is the hypothesized population standard deviation under the null hypothesis
Given:
- Sample size, n , is not provided.
- Sample standard deviation, s, is not provided.
- Population mean, [tex]\( \mu \)[/tex], is given as 680 days.
- Hypothesized population standard deviation, [tex]\( \sigma \)[/tex], is claimed to be less than 122 days.
Without the sample size and the sample standard deviation, it's not possible to directly calculate the chi-square test statistic. We would need either the sample size and the sample standard deviation or additional information about the distribution of the sample.
However, based on the information provided, we can still set up the null and alternative hypotheses. The null hypothesis (Hₒ) is that the population standard deviation is greater than or equal to 122 days, while the alternative hypothesis (H₁) is that the population standard deviation is less than 122 days.
Therefore, our hypotheses would be:
Null hypothesis (Hₒ): The standard deviation of electric bulbs manufactured by BIG Corporation is greater than or equal to 122 days.
Alternative hypothesis (H₁): The standard deviation of electric bulbs manufactured by BIG Corporation is less than 122 days.
We would then proceed with collecting additional data or obtaining the sample size and sample standard deviation to calculate the test statistic and make a conclusion about the null hypothesis based on the chi-square distribution.
