Question

3. Presently, the mean life expectancy of a rare strain of bacteria is 12 hours. A scientist claims that she has developed a medium and therefore disagrees with this hypothesis that it is not 12 hours. The scientist tests 25 cultures and finds that they have a mean life of 13.25 hours with a sample standard eviation = 2 hour. Do these results show that the medium is effective in increasing the bacteria's life expectancy? (Use 2 = 5%) a. State the null and alternative hypothesis b. Determine and draw the hypothesis test model (Label everything) c. Determine the critical value(s) and test statistic d. Determine the conclusion

Answer 1

Given that the mean life expectacny of a rare strain of bacteria is 12 hours

The scientist tests 25 cultures and find that they have a mean life of 13.25 hours with a sample standard deviation of 2 hours

So Sample mean = 13.25 hours

r

Sample Standard Deviation S = 2 hours

Sample size n = 25

The scientist claims that the mean life expectany is not 12 hours

Question (a)

Null Hypothesis H₀ : $1596104181659_blob.png$ = 12

Alternate Hypothesis H₀ : $1596104181622_blob.png$ $1596104181628_blob.png$ 12

The Null Hypothesised value is $1596104181614_blob.png$ ₀ = 12

Question (b)

Given that the mean life expectacny of a rare strain of bacteria is 12 hours

The scientist tests 25 cultures and find that they have a mean life of 13.25 hours with a sample standard deviation of 2 hours

So Sample mean = 13.25 hours

r

Sample Standard Deviation S = 2 hours

Sample size n = 25

Here we use one sample t-test since n is less than 30 and distribution is assumed to be normal

t-test statistic = (
r
- $1596104181561_blob.png$ ₀) / (S /
72
)

= (13.25 - 12) / (2 / $\sqrt{25}$ )

= 1.25 / (2 / 5)

= 1.25 / 0.4

= 3.125

Given significance level = 0.05

Number of degrees of freedom = n - 1

= 24

The critical t-value for 24 degrees of freedom at 0.05 significance level for a two-tailed test = 1.711

The p-value for a t-score of 3.125 and 24 degrees of freedom for a two-tailed test = 0.00460264 from online calculator

Question (d)

Since the test statistic of 3.125 is greater than the critical t-value of 1.711, we reject the Null Hypothesis H₀ and conclude that there is enough evidence at 0.05 significance level to support the scientist's claim that the mean life expectany is not 12 hours