ume that adults were randomly selected for a poll. They were asked if they "favor or oppose using federal tax dollars to fund medical research using stem cells obtained from human embryos." Of those polled, 485485 were in favor, 396396 were opposed, and 123123 were unsure. A politician claims that people don't really understand the stem cell issue and their responses to such questions are random responses equivalent to a coin toss. Exclude the 123123 subjects who said that they were unsure, and use a 0.100.10 significance level to test the claim that the proportion of subjects who respond in favor is equal to 0.50.5. What does the result suggest about the politician's claim? Identify the null and alternative hypotheses for this test. Choose the correct answer below. A. Upper H 0H0: pequals=0.50.5 Upper H 1H1: pgreater than>0.50.5 B. Upper H 0H0: pequals=0.50.5 Upper H 1H1: pnot equals≠0.50.5 C. Upper H 0H0: pnot equals≠0.50.5 Upper H 1H1: pequals=0.50.5 D. Upper H 0H0: pequals=0.50.5 Upper H 1H1: pless than<0.5

The null and alternative hypothesis for this question is H₀: p = 0.50 and H₁: p ≠ 0.50 respectively.

Hence, option B is correct.

Upper H0: pequals=0.5, Upper H1: pnot equals≠0.5

The hypothesis test shows that there is enough evidence to conclude that the proportion of the population that favour the use of federal tax dollars to fund medical research using stem cells obtained from human embryos is not 0.50 like that of a coin toss. That is, the politicians claim is false.

Step-by-step explanation:

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually contains the signs ≠, < and > depending on the directions of the test.

For this question, the politician claims that people don't really understand the stem cell issue and their responses to such questions are random responses equivalent to a coin toss. A coin toss has a 50-50 probability, with a proportion 0.5 for heads and another 0.5 for tails.

Hence, the null hypothesis for this question would be that there is evidence to suggest that the proportion of the population that favour the use of federal tax dollars to fund medical research using stem cells obtained from human embryos is 0.50 like that of a coin toss. That is, the politicians claim is true.

And the alternative hypothesis is that there is significant evidence to conclude that the proportion of the population that favour the use of federal tax dollars to fund medical research using stem cells obtained from human embryos is not 0.50 like that of a coin toss. That is, the politicians claim is false.

Mathematically, if p is the population proportion that favour the use of federal tax dollars to fund medical research using stem cells obtained from human embryos.

The null hypothesis is represented as

H₀: p = 0.50

The alternative hypothesis is represented as

H₁: p ≠ 0.50

To do this test, we will use the z-distribution because although, no information on the population standard deviation is known, the sample size is large enough for a z-test statistic to work.

So, we compute the test statistic

z = (x - μ)/σₓ

x = sample proportion = (485)/(485+396) = 0.55 (excluding the ones that were unsure)

μ = p₀ = The proportion we are comparing against = 0.50

σₓ = standard error = √[p(1-p)/n]

where n = Sample size = 485 + 396 = 881

σₓ = √[0.55×0.45/881] = 0.0167609874 = 0.01676

z = (0.55 - 0.50) ÷ 0.01676

z = 2.98 = 2.98

checking the tables for the p-value of this z-statistic

Degree of freedom = df = n - 1 = 881 - 1 = 880

Significance level = 0.10

The hypothesis test uses a two-tailed condition because we're testing in both directions (greater than or less than).

p-value (for z = 2.98, at 0.10 significance level, df = 880, with a two tailed condition) = 0.002882

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.10

p-value = 0.002882

0.002882 < 0.10

This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the proportion of the population that favour the use of federal tax dollars to fund medical research using stem cells obtained from human embryos is not 0.50 like that of a coin toss. That is, the politicians claim is false.

Hope this Helps!!!

part a

answer: a reasonable domain is where n is a real number. so n can be between 0 and 10. both endpoints are included.

work shown:

n is the number of days after the experiment starts. the smallest n can be is n = 0 which means that 0 days have gone by, and we're at the start. to find out how large n should be, then replace f(n) with 16.13 and solve for n. use logarithms to isolate the exponent.

f(n) = 12*(1.03)^n

16.13 = 12*(1.03)^n

16.13/12 = (1.03)^n

1.34416666666667 = (1.03)^n

(1.03)^n = 1.34416666666667

log[ (1.03)^n ] = log[ 1.34416666666667 ]

n*log[ 1.03 ] = log[ 1.34416666666667 ]

n = log[ 1.34416666666667 ]/log[ 1.03 ]

n = 10.0062999823929

this rounds to n = 10 which is fairly close but not 100% perfect. so this is the largest n can be.

note: if you plug n = 10 into f(n), you'll get roughly 16.127 which rounds to 16.13 (this comes up again in part c)

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part b

answer: the y intercept is 12. it represents the starting height of the plant in cm.

work shown:

plug n = 0 into the f(n) function. simplify

f(n) = 12*(1.03)^n

f(0) = 12*(1.03)^0

f(0) = 12*(1)

f(0) = 12

on day n = 0, aka the starting point, the height f(n) is 12 cm

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part c

answer: the average rate of change is approximately 0.43061036458991 (round however you need to). this represents the average growth rate from day n = 3 to day n = 10. so the plant grew roughly 0.43 cm per day during this timespan, assuming you round to 2 decimal places.

work shown:

compute f(3)

f(n) = 12*(1.03)^n

f(3) = 12*(1.03)^3

f(3) = 13.112724 < we'll use this later

compute f(10)

f(n) = 12*(1.03)^n

f(10) = 12*(1.03)^10

f(10) = 16.1269965521294 < we'll use this later

now use the formula below with a = 3 and b = 10

aroc = average rate of change

aroc = [ f(b) - f(a) ]/[ b - a ]

aroc = [ f(10) - f(3) ]/[ 10 - 3 ]

aroc = (16.1269965521294 - 13.112724)/(10 - 3)

aroc = 3.0142725521294/7

aroc = 0.43061036458991

round this however you need to

note: the plant grew approximately 3.01 cm over 7 days, so roughly 0.43 cm per day is the average growth rate (if you were to round to 2 decimal places).