Question

Create a Psychology stats question : step 1: make a frequency or grouped frequency distribution table, and do an interpolation to find some percentile. Part Two must require finding the Z-score and probability for a sample mean. Part Three must require doing some type of t-test and reporting the results in a sentence along with an effect size.

Please Each of these parts should include an 'experiment' scenario you make up.

please include answers to made up question.

Answer 1

Notice that the first class that exceeds 20% of the data is the second, therefore the 20th percentile is The Psychology and Health Group has published an article in which it is exposed that, in average, more than 80% of the people who commit suicide come from economic sectors whose income in the last fiscal year was at least $ 200,000, which makes us think that "the money does not buy happiness". To test if what the Psychology and Health Group says is true, an investigation has been done on 50 suicide cases selected randomly from the population and the amount of income that person (or his family group) had in the last one fiscal year has been recorded. The results are summarized in the following table P20 = LL+ 100--1 P20 = LL2+ f 50 - 204 *50 = 50 + 100 7 + Valur + = 50 + 9 +50 Since the 20th percentile is 92.86, then according to the sample, 80% of the people who were sucked had annual income of more than approximately $ 93,000. + Absolute frequency income in thousands of dollars LL 50 = 50 + 42.8571 = 92.8571 93 UP 0 50 100 100 150 200 250 300 150 200 250 300 350 Total To calculate the Z-score it is necessary to know the mean and the standard deviation of the population, but since we do not know them, we have to use the data from the extended frequency table to estimate them, then n = 50 Mean: Variance Ef + x-n.82 n - 1 1901250 - 50.1752 50 - 1 370000 49 s2 = 7551.020408 Standard deviation S = 5 s = 77551.02 s= 86.8966 As Psychology and Health Group indicates that more than 80% of the people who committed suicide had incomes greater than 200.000 dollars, it seems reasonable to look for the percentile corresponding to the 80% higher in our data. This is equivalent to calculating the 20th percentile. For this calculation, and another one later, the extended frequency table is presented below 50 X = 175 Midpoint Absolute frequency Accumulate d absolute frequency Fi x 25 income in thousands of dollars LL UP 0 50 100 100 150 150 200 200 250 250 300 300 350 Relative absolute frequency %F 8% 22% 40% 62% 76% In our case, it is interesting to know the probability that a person who has committed suicide had an income of more than $ 200,000, for this we will find the Z- score corresponding to 200, thus 2 200 - X 200 - 175 Z =- s/n 86.8966/50 = 2.0343 Therefore z-table PC > 200) = P(Z > 2.0343) 0.020958982 That is, according to our sample, only 2% of the people who committed suicide had incomes above $ 200,000. Finally, let's consider the following hypothesis test regarding the true proportion of individuals who had incomes above $ 200,000 to verify if what the Psychology and Health Group says is true. Then, using a significance a = 0.05 we have that fl f *x? 100 2500 525 39375 1125 140625 1925 336875 1575 354375 2200605000 1300 422500 8750 1901250 175 225 92% 275 325 100% Total- 50 -

SH: 1H, p = 0.8 p < 0.8 If the null hypothesis is true, then the T-score is Tapp The observed value for p P(1-p) n 0.02 -0.8 The reject region is given by RR = {T <tads) Here TE is distributed t- student with 1-1 - 49 degrees of freedom, then RR = {T < t0.05:40) RR = {T< -1.6766} P = P(> 200) p = 0.02 T= 10.8(1 -0.8) 50 -0.78 0.05656854 T= -13.7886 As can be seen, the test statistic T = -13.8 is less than the critical value to.05.40 = -1.68, therefore the null hypothesis is rejected that is, there is enough evidence in the sample to affirm that the true proportion of people who have committed suicide and who had income over $ 200000 is less than 80%