Right or leftMost people are right-handed, and even the right eye is dominant for most people. Molecular biologists have suggested that late-stage human embryos tend to turn their heads to the right. In a study reported in Nature (2003), German bio-psychologist OnurGüntürkün conjectured that this tendency to turn to the right manifests itself in other ways as well, so he studied kissing couples to see which side they tended to lean their heads while kissing. He and his researchers observed kissing couples in public places such as airports, train stations, beaches, and parks. They were careful not to include couples who were holding objects such as luggage that might have affected which direction they turned. For each kissing couple observed, the researchers noted whether the couple leaned their heads to the right or to the left. They observed 124 couples, ages 13–70 years. Suppose that we want to use the data from this study to investigate whether kissing couples tend to lean their heads right more often than would happen by random chance.

The symbol π represents the long-run proportion of all the couples that lean their heads
leftright

while kissing.

Which of the following best describes the null hypothesis and the alternative hypothesis using π?

null: π ≠ 0.5, alternative: π > 0.5
null: π = 0.5, alternative: π < 0.5
null: π = 0.5, alternative: π > 0.5
null: π ≠ 0.5, alternative: π < 0.5

Of the 124 kissing couples, 80 were observed to lean their heads right. What is the observed proportion of kissing couples who leaned their heads to the right? What symbol should you use to represent this value? (Round answer to 3 decimal places, e.g. 5.275)
p^=

the absolute tolerance is +/-0.001

Determine the standardized statistic from the data. (Hint: You will need to get the standard deviation of the simulated statistics from the null distribution.) (Round answer to 2 decimal places, e.g. 52.75)
z =

the absolute tolerance is +/-0.02

Interpret the meaning of the standardized statistic.

The observed proportion of couples who leaned to the right when kissing is 3.22 standard deviations above the null hypothesized value of 0.50.
The observed proportion of couples who leaned to the right when kissing is 3.22 standard deviations away from the null hypothesized value of 0.50.
The observed proportion of couples who leaned to the right when kissing is 3.22 standard deviations below the null hypothesized value of 0.50.

Select the best conclusion that you would draw about the null and alternate hypotheses.

We have strong evidence that the proportion of couples that lean their heads to the right while kissing is more than 50%.
We have strong evidence that the proportion of couples that lean their heads to the right while kissing is less than 50%.
We have strong evidence that the proportion of couples that lean their heads to the right while kissing is 50%.
We have strong evidence that the proportion of couples that lean their heads to the right while kissing is near to 50%.

Answers

Answer 1

Answer:

1) null: π = 0.5, alternative: π > 0.5

2)p^= 80/124 =0.645

std error =(phat(1-phat)/n)1/2 =0.0430

3)z = (phat-p)/std erro =(0.645-0.5)/0.0430 =3.22

4)The observed proportion of couples who leaned to the right when kissing is 3.22 standard deviations above the null hypothesized value of 0.50

5)We have strong evidence that the proportion of couples that lean their heads to the right while kissing is more than 50%

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Answers

Answer:

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Step-by-step explanation:

Answer:

x = 4; (4, –25)

Step-by-step explanation:

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(-3l^2w^3)(2lw^4) simplify express using exponents.

Answers

The simplified algebraic expression using exponents is $(-3l^2w^3)(2lw^4)$ simplifies to $-6l^3w^7.$

To simplify the given expression using exponents, follow these steps:

Multiply Coefficients: Multiply the coefficients (-3) and (2) to get -6.

Combine Like Bases: For the variables with the same base (l and w), add the exponents when they are multiplied together.

Here, $l^2 * l^1 = l^(2+1) = l^3$ , and $w^3 * w^4 = w^(3+4) = w^7.$

Final Simplified Expression: Combine the results from steps 1 and 2 to get $-6l^3w^7.$

Therefore, the simplified expression using exponents is $(-3l^2w^3)(2lw^4)$ simplifies to $-6l^3w^7$ .The expression has been simplified using the rules of exponentiation. This simplification helps in reducing the complexity of the expression and making calculations easier.

Learn more about algebraic expression here:

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Answer:

Step-by-step explanation:

(-3)(2)= -6

(l^2w^3)(lw^4) = l^3w^7

-6l^3w^7

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