SAT College

Assume 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, 487 were in​ favor, 402 were​ opposed, and 122 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 122 subjects who said that they were​ unsure, and use a 0.05 significance level to test the claim that the proportion of subjects who respond in favor is equal to 0.5. What does the result suggest about the​ politician's claim? Identify the null and alternative hypotheses for this test. Choose the correct answer below.

Answers

Answer 1
ANSWER -

We can use a hypothesis test to assess whether the politician's claim that people's responses to the stem cell issue are equivalent to a coin toss is supported by the data. We will exclude the 122 subjects who were unsure, as their responses do not provide information about their position on the issue.

The null hypothesis for this test is that the proportion of adults who favor using federal tax dollars to fund stem cell research is equal to 0.5, which is the same as the proportion who would respond randomly to the question. The alternative hypothesis is that the proportion who favor or oppose stem cell research is different from 0.5.

We can perform a one-sample proportion test using the following formula:

z = (p - P) / sqrt(P(1-P) / n)

where p is the sample proportion, P is the hypothesized proportion (0.5), and n is the sample size (487 + 402 - 122 = 767). The resulting test statistic, z, can be compared to the standard normal distribution to determine the p-value.

Plugging in the values, we get:

p = 487 / (487 + 402) = 0.548
z = (0.548 - 0.5) / sqrt(0.5 * 0.5 / 767) = 2.43
p-value = P(Z > 2.43) = 0.0076 (using a one-tailed test)

Using a significance level of 0.05, we can reject the null hypothesis because the p-value is less than 0.05. This means that the proportion of adults who favor stem cell research is significantly different from 0.5 and that the politician's claim that people's responses are random is not supported by the data.

Therefore, we can conclude that there is evidence to suggest that people have an opinion on the stem cell issue and that their responses are not equivalent to a coin toss.

Related Questions

What is the t-statistic?

Answers

In statistics, the t-statistic is the ratio of the departure of the estimated value of a parameter from its hypothesized value to its standard error. It is used in hypothesis testing via Student's t-test. The t-statistic is used in a t-test to determine whether to support or reject the null hypothesis.

ANSWER-

The t-statistic is a measure of the difference between the mean of a sample and the mean of the population, in units of the standard error. It is calculated by taking the difference between the sample mean and the population mean, dividing by the standard error of the mean, and then multiplying by the square root of the sample size.

The formula for the t-statistic is:

t = (sample mean - population mean) / (standard error of the mean)

The t-statistic is used in hypothesis testing to determine whether a sample mean is significantly different from a population mean. The t-distribution is used to calculate the probability (p-value) of observing a t-statistic as extreme as the one obtained from the sample, assuming the null hypothesis is true.

IF THE DIAMETER A CIRCLE . FIND ITS CIRCUMFERENCE . CALCULATOR'S VALUE OF . ROUND ANSWER TO THE NEAREST TENTH

Answers

ANSWER -

To find the circumference of a circle given its diameter, you can use the formula:

C = πd

where C is the circumference, d is the diameter, and π is a mathematical constant approximately equal to 3.14159.

If you have the diameter of the circle, simply multiply it by π to get the circumference.

For example, if the diameter of the circle is 10, the circumference would be:

C = πd
C = π(10)
C ≈ 31.4

Rounding the answer to the nearest tenth gives a final answer of 31.4 units.

The circumference of the circle is approximately 31.4 units.

To find the circumference of a circle, you need to know its diameter. The formula to calculate the circumference (C) of a circle is:

C = πd

Where π (pi) is a mathematical constant approximately equal to 3.14159, and d represents the diameter of the circle.

To find the circumference, you can multiply the diameter by π.

For example, if the diameter of the circle is 10 units:

C = π x 10

C ≈ 3.14159 x 10

C ≈ 31.4159

Rounding the answer to the nearest tenth, the circumference of the circle is approximately 31.4 units.

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some particular website, the password must start with A or B there must be 5 more characters, and each of the characters may be a numeric digit or letter of the alphabet how many diffrent passwords are possible

Answers

ANSWER -

If a password on a particular website must start with either A or B and must have 5 more characters that can be either a numeric digit or a letter of the alphabet, we can use the multiplication principle to calculate the total number of possible passwords.

Since the first character can be either A or B, there are 2 options for the first character. For each of those options, there are 36 options (26 letters + 10 digits) for the remaining 5 characters.

Using the multiplication principle, we can multiply the number of options for each position to get the total number of possible passwords:

2 (options for the first character) * 36^5 (options for each of the remaining 5 characters) = 2 * 60,466,176 = 120,932,352

Therefore, there are 120,932,352 different possible passwords that meet the requirements for this particular website.

In a family of 5 children what is the probability of have 1 boy and then 4 girls in that order. (Exclude multiple births and assume all outcomes)

Answers

Assuming that the probability of having a boy or a girl is equal (i.e., 0.5), the probability of having 1 boy and 4 girls in that order in a family of 5 children can be calculated as follows:

P(1 boy, 4 girls) = P(boy) x P(girl) x P(girl) x P(girl) x P(girl)

where P(boy) is the probability of having a boy and P(girl) is the probability of having a girl.

Therefore, we have:

P(1 boy, 4 girls) = 0.5 x 0.5 x 0.5 x 0.5 x 0.5 = 0.5^5

= 0.03125 or 3.125%

So, the probability of having 1 boy and 4 girls in that order in a family of 5 children is 3.125%.


When I have an ? in something, it is easy to learn.

Answers

When I have an interest in something, it is easy to learn.

How can interest affect learning?

When you approach learning with a passive or disinterested attitude, it can be difficult to retain information or apply it in real-world situations.

So embracing your natural curiosity and actively seeking out answers to your questions is a great way to make learning easier and more enjoyable as you already have a genuine interest in it and would want to learn more about it.

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