Question

Using the entire data set of 65 stocks, count up the number of stocks in your data that have a high stock price that is at least $20. State this value here:

Verify this by copying the stem-and-leaf display for the high prices below.

Stem and Leaf Plot of High   Leaf Digit Unit = 10            Minimum  1.1400 3 9 represents 390              Median   27.930                                 Maximum  393.00 Depth   Stem  Leaves   (46)     0   0000000000000001111111111122222222223333344444    19       0   5677888999     9       1   23     7       1   6     6       2   0003     2       2   8     1       3        1       3   9 65 cases included   0 missing cases

1. Suppose it is desired to determine if the true percentage of all stocks that have high prices that are at least $20 differs from 40%. Is the sample size large enough to conduct this test? Why or why not? Show your calculations for full credit!
2. Use the table on the next page to locate the number of your stocks with high prices of at least $20 in your sample. Use the table to locate the Test Statistic that you should use for this test and write it here:Test Statistic: _______
3. Give the rejection region for this test (you choose an acceptable level for a)

4. In the words of the problem, give a practical conclusion for this test. Make sure to include your choice of α in this conclusion.

Answer 1

Answer:

Given Data

From the stem plot , the number of stocks that is at least $20 = 34(Assuming as per question not given)

a)Suppose it is desired to determine if the true percentage of all stocks that have high prices that are at least $20 differs from 40% .

The necessary condition for the normal distribution of the proportion is ,

Since the sample size is 65 which is larger than 25 we take an assumption that the sample distribution of proportion values follows a normal distribution.

b) Use the table on the next page to locate the number of your stocks with high prices of at least $20 in your sample.

Test statistic

The point estimate of the proportion of high stock price , p =

= 0.5231

The z statistic is obtained using the formula.

z = 2.026

c) Give the rejection region for this test .

Let the significance level = 0.05

This is a two tailed test

The critical values for the significant level = 0.05 are obtained from the standard normal distribution table.

Upper critical value

  

= 1.96

Lower critical value

  

= -1.96

Rejection region , R =

The rejection lies above the upper critical value and below the lower critical value.

d) In the words of the problem , give a pratical conclusion for this test .

Since the z statistic = 2.03 is greater than 1.96 at a 5% significance level , there is sufficient evidence to conclude that the true percentage of all stocks that have high prices differs from 40%.

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