Question

a) After taking a sample of 300 rice plants, you find the frequency of the betaine aldehyde dehydrogenase gene (BADH2) allele conferring aroma to rice grains such as basmati or jasmine to be 93 (out of 600 alleles total), leading to an estimated mean proportion of 0.15 with 95% confidence interval of 0.13, 0.19. Which of the following statements is correct regarding this CI?

	a	The true population proportion lies between 0 and 1, but between 0.13 and 0.19 there is higher probability of truth.
	b	There is a 95% probability the interval between 0.13 and 0.19 contains the true population proportion.
	c	There is a 95% probability the true population proportion lies between 0.13 and 0.19.
	d	There is a 95% probability the true population proportion includes 0.13 and 0.19.
	e	The 99.99% confidence interval would be closer to the true value.

b) Does the class have low or high white blood cell count? The white blood cell count of a sample of 12 students is taken, finding the sample has a mean of 10 million leukocytes/mL and a standard deviation of 5. Given that the mean in healthy humans is 7.5, does the mean from the sample differ from the healthy human mean?

	a	No, and I solved it using an unpaired two-sample t-test
	b	Yes, and I solved it using a paired two-sample t-test
	c	No, and I solved it using a paired two-sample t-test
	d	No, and I solved it using a one-sample t-test
	e	Yes, and I solved it using an unpaired two-sample t-test

Answer 1

Answer:

a)

Given,

n = 600, x = 93

Here,

p^ = 0.15

There is a 95% probability the interval between 0.13 and 0.19 contains the true population proportion.

So option B is correct answer.

b)

Given,

Null Hypothesis Ho : mean = 7.5

Alternative Hypothesis H1 : mean 7.5

test statistic is given below

t = xbar - mean /(s/sqrt(n)

substitute the values

= 10 - 7.5 /(5/sqrt(12)

t = 1.732

degrees of freedom = n - 1

= 12 - 1

df = 11

Significance Level (alpha) = 0.05

Here the P-Value is 0.1112

Since p value is greater than significance level, So hence we fail to reject H0 null hypothesis

We conclude that,

No, and I solved it using a one-sample t-test

i.e.,

Option D is correct answer.