1) A stock market analyst wants to determine if the recent introduction of the IPhone 8x has changed the distribution of shares in the cellphone market. The analyst collects data from a random sample of 500 cellphone customers. The table below shows the observed customers' cellphones (f_i) and market shares. When using this random sample the analyst needs to be 99% confident of the   test results. The hypothesis to be testedfollows:

H₀: P_lg=0.25; P_a=0.40; P_s=0.35 ; market shares have remained same H_a: P_lg≠0.25; P_a≠0.40; P_s≠0.35 ; market shares have changed

Cellphone company Current Market Share Observ.f_i

Samsung 0.35 200

Apple 0.40 210

LG 0.25 90

Totals 500

a. Perform a chi-squared test to find out whether the market shares havechanged.

b. After the test, would you conclude that the introduction of the IPhone 8x has changed the cellphone market share composition?WHY?

2) The Scholastic Aptitude Test (SAT) contains three sections: critical reading, mathematics and writing. Each part is scored on a 500-point scale. Information on test scores for the 2017 version of SAT is available at the College Board website. A sample of SAT scores for 5 students follow:

SAT scores - 2017

Student Reading Math Writing

1 460 458 463

2 456 459 455

3 454 460 461

4 460 458 458

5 455 455 458

Sample mean 457 458 459

Sample Variance 13.8 14.7 60.3

a. You are hired as statistician to test whether there are any differences among the three sections of the SAT, allowing for 10%error.

b. The level of difficulty for all the three sections of the SAT, measured by the score, are supposed to be the same. Do you agree with this after the results of the test? WHY?

3) The U.S. Census Bureau computes quarterly vacancy and homeownership rates by state and metropolitan statistical areas. The following table shows the rental vacancy rates in percentage (%) grouped by region for the last quarter of 2017 using a sample of 4 statistical metropolitanareas.

Source of variation Sum of Squares (SS) Degrees of freedom Mean Square (MS) F

Treatment 8 2 4 4.36

Error 11 12 0.92

Total 19 14

 ANOVA TABLE

                          Vacancy rates(%)          

              Region   Northeast      South   West

1              6            5        8

2              6            9        9

3              5            6        7

4              7            8        8

 sample

mean       6            7        8

a. Conduct a Fisher testallowing for 5% error.

b. According to the result of your test, did you find differences in vacancy rates in these regions? WHY?