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:_29 Verify this by copying the stem-and-leaf display for the high prices below. Student Edition of Statistix 10.0 4/22/2020, 10:55:54 AM Stem and Leaf Plot of Hight Leaf Digit Unit = 10 Minimum 2-2600 39 represents 390 Median 26.990 Maximum 393.00 Depth Stem Leaves (45) 0 000000000011111111111111111112222233344444444 0 566788889999 5667 65 cases included Omissing cases 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%. Is the sample size large enough to conduct this test? Why or why not? Show your calculations for full credit! 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. Use the table to locate the Test Statistic that you should use for this test and write it here: Test Statistic: 0.76 C. Give the rejection region for this test (you choose an acceptable level for a). d. In the words of the problem, give a practical conclusion for this test. Make sure to include your choice of a in this conclusion

Answer 1

Ans: From The Slem plot , the number of stocks that at least $ 20 = 29 a). The necessary condition for the normal distribution of the proportiones, np 210 n*0.40 Zlo → n2 25 Since the Sample size is 65 which is larger than 25, we fake an assumption that the sample distribetion of proportion values follows a normal distribution . b) Test Statistic: The point estimate of the proportion of high stock price P= 29 - 0.4461 GS The Z- Statistic as obtained using the formula, 0.4461 -0.40 ZE P-Po V 65 fpoll-Po 12 = 0.4586 10.40(1-0.40) [6.76 c. Let the significance level = 0.05 This as a two-tüled test The critical values for the significance level -0.05 are are obtained from the Standard normal distribution table opper critical value = c=21-072-21-0.05 –20.935 = 1.96 lower critical value = 2c =266 = 20.05-20.025 =1.96 Rejection region, R= 2: $1=1> 1996}

The rejection and lies above the upper entical value below the lower critical Kelue.' ď). Since the zostalistic = Q.76 0.76 ºs - less than 1.96 at a 5% level of significance there ah Sufficent) eurde & not enough evidence to conclude that the true percentage of that have high prices offers not differs from 40% .
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