Aresearcher is interested in determining if a psychic really has power to predict. the researcher takes four cards, each of a different type: king, queen, jack, and ace. after mixing up the cards many times and he selects one card without showing the psychic. the researcher asks the psychic which card was selected. the researcher records if the psychic was correct or not. the researcher does this two hundred times. if the psychic really has special abilities then he should pick the correct card more often then if it was by chance alone. the researcher is interested in determining if the card was identified correctly significantly more often then chance would suggest. what would be the null and alternative hypothesis for this case

D

Explanation:

a)  

b)  

Step-by-step explanation:

Data given and notation

n=180 represent the random sample taken

X=43 represent the correct guesses

estimated proportion correct guesses

is the value that we want to test

represent the significance level

z would represent the statistic (variable of interest)

represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the ture proportion is higher than 0.2 or no.:  

Null hypothesis:  

Alternative hypothesis:  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

(1)  

The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value .

Part a: Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

Part b: Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

a. The Z-statistic is and the observed value 1.591

b. p-value: 0.0558

Step-by-step explanation:

To see if there is evidence that the psychic is doing better than just guessing, we want to test the next hypothesis

vs (upper-tail alternative)

We have a large sample size of n = 200 trials. Therefore, the test statistic is given by

which is normally distributed.

The observed value is  

.  

The p-value is calculated as P(Z > 1.591) = 0.0558. With this p-value we fail to reject the null hypothesis at the significance level of 0.05 for instance.

B.

Explanation:

Psychic Distance can be defined as a distance between the narration and the thoughts of the character. Psychic distance is also known as Narrative Distance or Emotional Distance. The concept of Psychic Distance was developed by John Gardner in his book titled 'The Art of Fiction.' Narrative distance defines the distance between the narrative and the reader to the character.

In the given statement, the psychic distance is large. It is because there is no emotional connection yet between the characters and the readers. There is a large distance between the narrative and the characters.

Thus option B is correct.

C. P- value

Step-by-step explanation:

hello,

we were given the sample size, n = 200

also the probability that the psychic correctly identifies the symbol on the 200 card is

using the large sample Z- statistic, we have

   =

    = 1.7678

thus the P - value for the hypothesis test is P(Z > 1.7678) = 0.039.

from the above, we conclude that the P- value

no ; a negative

Explanation:

Correlation: It means alliance, measure of the degree to which two different variables are related to each other.

Negative correlation: The relationship between two different variables in which the decrease in one variable leads to an increase in the other variable. When two different variables have a negative correlation, then they possess an inverse relationship.

Correlational studies are being conducted, where experimenting is not possible.

Psychic numbing is a tendency for people or societies to withhold focus from stressful past events, or from potential risks that are considered to have massive, but low possibility, effects.

The 95% confidence interval would be given (0.172;0.288).  

We are confident at 95% that the true probability that the psychic correctly identifies the symbol on the card in a random trial is between (0.172;0.288).  

We can conclude that her random guessing would have got her correct 20% of the time. Since the confidence interval contains 0.2, she has no psychic powers, rather she just guessed it like normal people. Any person could have got it correct this many times.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

Description in words of the parameter p

represent the probability that the psychic correctly identifies the symbol on the card in a random trial

represent the estimated probability that the psychic correctly identifies the symbol on the card in a random trial

n=200 is the sample size required  

represent the critical value for the margin of error  

The population proportion have the following distribution  

Numerical estimate for p

In order to estimate a proportion we use this formula:

where X represent the cases successful

represent the estimated probability that the psychic correctly identifies the symbol on the card in a random trial

Confidence interval

The confidence interval for a proportion is given by this formula:

For the 95% confidence interval the value of and , with that value we can find the quantile required for the interval in the normal standard distribution.  

And replacing into the confidence interval formula we got:  

And the 95% confidence interval would be given (0.172;0.288).

We are confident at 95% that the true probability that the psychic correctly identifies the symbol on the card in a random trial is between (0.172;0.288).  

We can conclude that her random guessing would have got her correct 20% of the time. Since the confidence interval contains 0.2, she has no psychic powers, rather she just guessed it like normal people. Any person could have got it correct this many times.

think of the word "numb"

Explanation: