Question

A set of solar batteries is used in a research satellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance σ2 of lifetimes of these batteries affects the useful lifetime of the satellite before it goes dead. If the variance is too small, all the batteries will tend to die at once. Why? If the variance is too large, the batteries are simply not dependable. Why? Engineers have determined that a variance of σ2 = 23 months (squared) is most desirable for these batteries. A random sample of 30 batteries gave a sample variance of 16.3 months (squared). Using a 0.05 level of significance, test the claim that σ2 = 23 against the claim that σ2 is different from 23.

Answer 1

Hence, we reject H_0 as There is sufficient evidence to show that population variance is not 23

Explanation:

From the question we are told that:

Sample size
`n=30`

Variance
`\sigma= 16.8`

Significance Level
`\alpha=0.05`

`\sigma = 23`

Genet=rally the Hypothesis are as follows

Null
`H_0=\sigma^2=23`

Alternative
`H_a=\sigma^2 \\eq 23`

Generally the equation for Chi distribution t is mathematically given by

t test statistics

`X^2=((n-1)\sigma)/(\sigma^2)`

`X^2=((30-1)16.8^2)/(23)`

`X^2=355.86`

Therefore

Critical Value

`P_(\alpha,df)`

Where

`df=29`

`P_(\alpha,df)=16.0471 and 45.7223`

`X^2=45.7223`

Hence, we reject H_0 as There is sufficient evidence to show that population variance is not 23