Mathematics, 25.03.2020 05:14, kluckey3426

The bacterial strain Acinetobacter has been tested for its adhesion properties. A sample of five measurements gave read- ings of 2.69, 5.76, 2.67, 1.62 and 4.12 dyne-cm2. Assume that the standard deviation is known to be 0.66 dyne-cm2 and that the scientists are interested in high adhesion (at least 2.5 dyne-cm2). a. Should the alternative hypothesis be one-sided or two-sided

Answers: 3

Show answers

Answers

answered: tishaadams2160

Part a

We need to conduct a one tailed test

We need to conduct a hypothesis in order to check if the mean is higher than 2.5, the system of hypothesis would be:

Null hypothesis: $\mu \leq 2.5$

Alternative hypothesis: $\mu 2.5$

Part b: Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{3.372-2.5}{\frac{0.66}{\sqrt{5}}}=2.954$

Part c :P-value

Since is a one sided test the p value would be:

p_v =P(z2.954)=0.0016

Conclusion

If we compare the p value and the significance level assumed $\alpha=0.01$ we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, we can conclude that the true mean is higher than 2.5 at 1% of signficance.

Step-by-step explanation:

a. Should the alternative hypothesis be one-sided or two-sided?

b. Test the hypothesis that the mean adhesion is 2.5 dyne-cm².

c. What is the P-value of the test statistic?

Data given and notation

Data: 2.69, 5.76, 2.67, 1.62 ,4.12

We can calculate the sample mean with this formula:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$\bar X=3.372$ represent the sample mean

$\sigma=0.66$ represent the population standard deviation

n=5 sample size

$\mu_o =2.5$ represent the value that we want to test

$\alpha=0.01$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

p_v represent the p value for the test (variable of interest)

Part a: State the null and alternative hypotheses.

We need to conduct a one tailed test

We need to conduct a hypothesis in order to check if the mean is higher than 2.5, the system of hypothesis would be:

Null hypothesis: $\mu \leq 2.5$

Alternative hypothesis: $\mu 2.5$

If we analyze the size for the sample is < 30 but we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (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".