Question

Randomly pick eight stocks from the newspaper. Using two consecutive days’ business sections, test whether the
stocks went down, on average, for the second day.
a) Find H0 and Ha.

b)What distribution should be used for the test

c) In words, define the random variable.

d) The distribution to use for the test is _____________.

e) Calculate the test statistic using your data.

f) Draw a graph and label it appropriately. Shade the actual level of significance.

g) Calculate the p-value:

h) Do you reject or not reject the null hypothesis? Why?

i) Write a clear conclusion using a complete sentence.

This is the data that I got for the stocks. Please help with answers for a to i.

	9-Jul	10-Jul
Coca Cola (KO)	43.92	45.15
Pepsi Cola (PEP)	132.71	134.46
CVS (CVS)	61.29	62.65
Walgreens (WBA)	39.01	40.12
Home Depot (HD)	247.96	250.11
Lowes (LOW)	135.61	137.43
Bestbuy (BBY)	84.95	84.9
Target (TGT)	117.91	118.86

Answer 1

We want to test for a sample where are comparing same subjects like a before and after test result. So these sample data sets are related / dependent. To test for the mean difference we will use a dependent samples t-test. The claim to test is wheter stocks have fallen. That is before > after (d > 0) This one sided right tailed test.

	09-Jul	10-Jul	d	d2
Coca Cola (KO)	43.92	45.15	-1.23	1.5129
Pepsi Cola (PEP)	132.71	134.46	-1.75	3.0625
CVS (CVS)	61.29	62.65	-1.36	1.8496
Walgreens (WBA)	39.01	40.12	-1.11	1.2321
Home Depot (HD)	247.96	250.11	-2.15	4.6225
Lowes (LOW)	135.61	137.43	-1.82	3.3124
Bestbuy (BBY)	84.95	84.9	0.05	0.0025
Target (TGT)	117.91	118.86	-0.95	0.9025
Total			-10.32	16.497

Mean =

SD =

Mean	-1.29
SD	0.6745
n	8

a) Find H0 and Ha.

(The stocks are same or have increased the next day on an average)

(The stocks are have decreased the next day on an average)

b)What distribution should be used for the test

Dependent samples t-test

T-distribution

c) In words, define the random variable.

Since we are concerned with the difference, the variable is the difference between the prices

d: The difference between the stock price of current and previous day

d) The distribution to use for the test is __t-dist.

e) Calculate the test statistic using your data.

Test stat:

Where the null mean = d₀ = 0

Test Stat = -5.4098

f) Draw a graph and label it appropriately. Shade the actual level of significance.

Level of significance = 0.05

C.V. =

=t_7,0.05

   = 1.8945 ......C.V. =

To reject the null hypothesis if Test Stat > C.V. for right tailed test

Since Test Stat < C.V.

We do not reject the nullhypothesis .

We see that red region is critical and test stat falls out side it.

g) Calculate the p-value:

p - value = P( >tes Stat)

=P(t₇> -5.41)

=1 - P((t₇> 5.41)

=1 - 0.0005

Ans: 0.9994

h) Do you reject or not reject the null hypothesis? Why?

We do not reject the null hypothesis as

p-value > 0.05 and Test Stat <C.V.

i) Write a clear conclusion using a complete sentence.

There is insufficient evidence to conclude that stocks went down, on average, for the second day.

If the test was left tailed means testing if stocks went up or 2 tailed test then we would have rejected it.