Provide answers only in space provided, do not attach additional sheets. Write d

Question

Provide answers only in space provided, do not attach additional sheets. Write dearly to ensure full credit for your answers Write the first letter of your surname in box above. Consider a population of frogs living on an island. We believe that the frogs may be members of a speeds call Pippins. The mean length of Pippins is known to be 11 cm the following length values (cm) were obtained for a sample of individuals from the island: 9.7 9.9 11.2 11.5 12.5 10.7 11.9 10.6 10.1 9.8 11.2 106 9.6 11.2 9.3 11.1 10.3 10.1 8.9 103 Do these frogs have sizes that are consistent with their being Pippins or not? Base your decision on whether the mean length of the island frogs is as expected Use the grammar described in lecture and slate with what degree of confidence you make your conclusion by providing the most specific range of p values from the table provided in lecture. You must use the phrase "significantly smaller", "significantly larger" or "not significantly different" in your answer. A researcher is investigating the possibility that a newly isolated alkaloid may work as a preleased and speed up the degradation of proteins. She measures the mean time it takes for a standard sized protein plaque to dissolve in a solution of 1% alkaloid and 99% water (min). Previous studies have confirmed that the mean time to dissolve in 100% water is 28 minutes, her times are: 26.3 26 4 28.3 25.9 28.6 28.4 28.4 29.4 28.4 29.9 26.5 27.7 26.0 24.7 24.8 28.0 Does this alkaloid seem to act as a protease? Base your decision on whether the dissolving time is less than expected and perform the correct test to answer this specific questions. Use the grammar described in lecture and state with what degree of confidence you make your conclusion by providing the most specific range of p values from the table provided in lecture. You must use the phrase 'significantly smaller", "significantly larger" or "not significantly different" in your answer.

Explanation / Answer

Question 2

Here, we have to use one sample t test for the population mean. The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: µ = 11

Alternative hypothesis: Ha: µ 11

This is a two tailed test.

We assume the level of significance or alpha value as 5% or 0.05.

We are given

Sample size = n = 20

Degrees of freedom = n – 1 = 20 – 1 = 19

From the given sample, we have

Sample mean = Xbar = 10.53

Sample standard deviation = SD = 0.9043

The test statistic formula is given as below:

Test statistic = t = (Xbar - µ) / [SD/sqrt(n)]

Test statistic = t = (10.53 – 11) / [ 0.9043/sqrt(20)]

Test statistic = t = -2.3491

P-value = 0.0298

Alpha value = 0.05

P-value < Alpha value

So, we reject the null hypothesis

At 5% level of significance, we conclude that there is no sufficient evidence that the mean length of Rana Pipiens is 11 cm. The population mean length of Rana Pipiens is significantly different from 11 cm at 5% level of significance.

Question 3

We have to perform one sample t test for the population mean.

H0: µ = 28 versus Ha: µ < 28

(One tailed test – left tailed test)

t = (Xbar - µ) / [SD/sqrt(n)]

Xbar = 27.35625

µ = 28

SD = 1.574788346

n = 16

df = n – 1 = 15

t = (27.35625 – 28)/[ 1.574788346/sqrt(16)]

t = -1.6351

P-value = 0.0614

Alpha value = 0.05

P-value > Alpha value

So, we do not reject the null hypothesis

We conclude that there is no sufficient evidence that the mean time is significantly smaller than 28 minutes.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.