2. the walton college of business was ranked 24th out of all public business schools in the united states in 2005. the dean attributes this success to the academic rigor of a new core curriculum of the program. in the past, business students averaged 6.8 hours/week studying with a standard deviation of 2.2 hours. the dean wonders if students under the new curriculum are studying more than the previous students. a random sample of 100 business students finds a sample average of 7.2 hours studying. perform the hypothesis tests for the dean at a 0.05 significance level. a. state your null and alternative hypotheses. b. use the critical value approach to assess whether you should reject or fail to reject your null hypothesis. i. calculate your z-statistic: ii. identify your critical value: iii. state your conclusion: c. compute the p-value for your z-statistic. what do you conclude when comparing your p-value to your alpha (α)? i. p-value: ii. conclusion:

See steps below

Step-by-step explanation:

a)

The null hypothesis is what is already established by previous researches  

Business students average 6.8 hours/week studying.

the alternative hypothesis tries to see how accurate is this based on new evidence. Since the sample averaged 7.2 hours studying, this gives us a base to contrast the hypothesis.  

Business students now average more than 6.8 hours/week studying.

As we can see, this is a right-tailed test.

b)  

For a 0.05 significance level, the critical value is the value such that the area under the Normal curve N(0;1) to the right of is less than 0.05. This is a very well-known value that can be found by looking up a table or with the computer.

=1.64

If our z-statistic is greater or equal to 1.64 we have reasons to reject the null and accept the new average.

i.

Our z-statistic is given by the formula

where

is the mean of the sample

is the mean of the null hypothesis

is the standard deviation

n is the sample size

Our z-statistic is then

ii.

As we already said, our critical value is 1.64

iii.

Since our z-statistic is greater than the critical value, we reject the null hypothesis and accept 7.2 hours/week as the new average.

c)

The p-value for our statistic is the area under the Normal N(0;1) to the right of our z-statistic. (see picture attached).

This area can be calculated either with tables or computer-assisted and is 0.0345.

Comparing our p-value 0.0345 against the level of significance we see that

p-value < level of significance

Conclusion: when the p-value is less than the level of significance we can reject the null.

Remark:

Rejecting the null does not mean that the null is false or the alternative is true. It only means that the probability we had made a mistake by a random sampling error or other reason is less or equal than the p-value.

see below

step-by-step explanation:

7.   there are 10 data points in the set.   the middle point is between 5 and 6.   the middle point in the top half is 8   and the middle point in the bottom half is 3. to find the iqr , take point 8 and subtract point 3

mid term   point 8 = 100   point 3 = 88

iqr = 100-88 = 12

final   point 8 = 93   point 3 = 78

iqr = 93 - 78 = 15

the final has the greatest iqr

6.   b - there is a high data value that causes the data set to be asymmetrical for the males: the data for males are high and asymmetrical .   there is an outlier for the males that skews the data

5.   the   iqr is a better measure of spread for the movies and basketball games.   since the basketball game has an outlier, we do not want to use standard deviation for measurement.  

3.   the exam median is much higher than the class median.   the median line is farther to the right on the exams

2.   there is no way to tell what the means are from the box and whisker plots.  

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.