Question

GreenBeam Ltd. claims that its compact fluorescent bulbs average no more than 3.24 mg of mercury. A sample of 25 bulbs shows a mean of 3.29 mg of mercury.

(a) State the hypotheses for a right-tailed test, using GreenBeam’s claim as the null hypothesis about the mean.

Answer 1

Null hypothesis:
`\mu \leq 3.24`

Alternative hypothesis:
`\mu > 3.24`

Explanation:

1) Previous concepts and data given

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

A right tailed test (sometimes called an upper test) is when the alternative hypothesis statement contains a greater than (>) symbol.

`\bar X=3.29` represent the sample mean

s represent the sample standard deviation

n represent the sample selected

`\alpha` significance level

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean for fluorescent bulbs is no more than 3.24 mg of mercury, the system of hypothesis would be:

Null hypothesis:
`\mu \leq 3.24`

Alternative hypothesis:
`\mu > 3.24`

IIf we know the population deviation we can apply a z test to compare the actual mean to the reference value, and the statistic is given by:

`z=(\bar X-\mu_o)/((\sigma)/(√(n)))` (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".