Discuss the below:
Q1. Car manufacturers have to publish an estimated MPG for each model production. Prior to manufacturing 'Car A° the manufacturer stated that the MPG Is 34. Post production the manufacturer has tested the MPG based 100 highway trips under varying conditions where the MPG is calculated at the end of each trip). Develop a hypothesis and state the type of statistical test that would be used to test or prove that the MPG is greater than 34. This Is a new model and there are no known estimates of the variance. Draw the distribution with critical value at S% alpha. (note: you cannot serve the problem, I'm looking for the correct hypothesis set up and rejection region)
Q2. A group of University of liadda psychologist Investigated the effects of age and gender on the
short-term memory of adults (Copmkke aging Confreente, Aaal 1996). Each in sample of 152 adults was asked to six* 20 common household items (eyeglasses, keys, hat. hammer, etc) Into the rooms of a computer-imaged house. After performing some unrelated artiGties. each
subject was asked to recall the locations of the objects they had placed. The correct responses were recorded.
a. The researchers theorized that women will have a higher mean recall score than men. Set up the null hypothesis:
b. The 43 men In the study had a recall score of 13.5 while the 109 women had a mean recall score of 14.4. The test statitstks resulted with a p.value of 0.0001. Interpret the resorts based on the hypothesis in (a).
c. The second part of the study was testing the effect of age. They theorized that younger adults would have a higher mean recall score than older adults Set up the null and alternative hypothesis:
d. The p value observed for the two means(ols vs young) is 0.0001.With what conclude and interpret the results based on the hypothesis in (c)
The following questions refer to the dataset available
Q3. Is there any correlation between 10 and Total grain Volume? What h the linear correlation coefficient?
Q4. We ere Interested In Padre 044 Whether or not brain the and body weight hose rehrtihrMAIP with a person's Ka fn a roultVe Poem regression model using BodyW00% end Total grain VoSame as the endanatory variables. Answer the followin evestiens:
a. What's the proportion of variation? Interpret.
b. How many betas bk, are there? What are they?
c. Do the betas have a positive or negative effect? The sign of beta indicates the effect of the variable on the person's IQ,explain the effect of each beta(i.e.,if the sign is negative,what does the mean?)
d. Are the explanatory variables predictive in other words. are they significant? if not why?
e. What conclusion can you make about this model
f. What conclusion can you make about the relationship between IQ and a person's total brain colume and body weight
Q5. Ina Time/CNN survey. 24% If 20$ single women said that they 'definitely want to get married.' In the same survey, 27% of 260 single men gave that same response. Use a 0.01 significance level to test the claim that there Is a difference between the proportion of men and the proportion of women vAto definitely want to gat married.
a. Hypothesis:
b. Critical Value
c. Test Statbtk
d. P-Value
e. Conclusion
Q6. The Journal of Visual Impairment and Blindness (may-jun.1997) published a study of the West*, of visual impaired students. Using diaries. the students kept track of several variables. Mich.:Ong number of hours of steep obtained M a typical day. These visually impaired students had a mean of 9.06 hours and a standard deviation of 2.11 hours. Assume that the distribution of the number of hours of sleep for this voup of student is approximately normal.
a. find the probability that a visually impaired student obtains less than Shows of sleep on a typical day.
b. find the probability that a visually impaired student gets between 8 and 10 hours of sleep on a typical day.
c. Twenty percent of all visually impaired students obtain less than how many hours of sleep on a typical day?