Please may I get some help with these few questions
Assignment 02 ASSIGNMENT 02 Unique Nr.: 698302 Fixed closing date: 20 JULY 2021 QUESTION 1 In the year 2014, there was a heavy advertising and the manager had three brands: Brand A microwaves had 45% of the market, brand 3 had 35%, and brand C had 20% of the market. A random sample of appliances stores shows that of 10 000 microwaves sold, 4350 were for brand A, 3450 were for brand B, and 2200 were for brand C. The manager wants to determine at the 1% level of significance to whether the data provides sufficient evidence to conclude that the market has changed. The test statistic is 1. 25.7143 2. 9.210 3. 2.5714 4. 30.987 5. 257143 QUESTION 2 Consider a multinomial experiment involving 100 trials and 3 categories. The observed frequencies resulting from the experiment are shown in the following table. lCategory 1 2 Bl Frequency 38 35 2'? The hypotheses are H0 : p1 = 0.45, p; = 0.30, p3 = 0.25 against H1 : At least two proportions differ from their specified values. The correct expected frequencies values are 1. 38 3S 2'? 45 3O 25 38 70 81 30 45 25 91:59?!\" 0.45 0.30 0.25 QUESTION 3 Consider the table below providing a breakdown of the responses of the employees based on their age. The manager of these employees want to determine if there is sufficient evidence that the level of job satisfaction is related to the age? Use a = 0.10. Response Age Very Interesting Fairly Interesting Not Interesting Under 30 31 24 13 Between 30 and 50 42 30 4 Over 50 32 21 3 Which one of the following statements is incorrect? 1. Ho : Job satisfaction and age are independent. 2. H1 : Job satisfaction and age are dependent. 3. The rejection region is {x2 > 1310.4 = 7.78}. 4. The value of the test statistic is 12 = 9.692. 5. Conclusion: fail to reject the null hypothesis at the 10% level of satisfaction therefore the job satisfaction is not related to the age. QUESTION 4 Consider a multinomial experiment with n = 150 trial and k = 4 cells. The observed frequencies and the null hypothesis to be tested are as indicated below: H0 : p1 = 0.15 p2 = 0.40 p3 = 0.35 p4 = 0.10. Cell 1234 The test statistic is 1. 21.7492 2. 12.4729 3. 7.81 4. 11.5643 5. 18.221157i QUESTION 5 The proportions of blood phenotypes A, B, AB and 0 from a population of the Eastern Cape Province are 0.41, 0.10, 0.04 and 0.45, respectively. To determine if the population proportions fit the reported probabilities, a sample of 200 residents was selected and their blood phenotypes were recorded. The observed frequencies are presented in the following table: |A 3 AB 0| 891812 81 The hypotheses are: Ho : p1 = 0.41, p2 = 0.10, p3 = 0.04, p4 = 0.45. H, : At least two proportions differ. Use the 10% level of significance to test the null hypothesis H0, the incorrect statement is: 1. The test statistic value is 3.6976. 2. The degrees of freedom is 3. 3. The critical value value is 6.25. 4. The null hypothesis is not rejected at the 10% level. 5. The expected frequencies are 82 20 8 90. QUESTION 6 A survey was carried out amongst 200 teenagers (of both genders and the between of 13 and 16 years) in various bookstores. Teenagers were randomly selected and the following question was asked: \"Which one of these three magazines do you most prefer to read?\". The magazine preference responses by gender is summarised in the table below: Observed frequencies Gender Magazine preference Total Beat Youth Grow Female 13 28 39 80 Male 33 45 42 120 Total 46 73 81 200 Which one of the following statements is correct? 1. Ho : There is an association between gender and magazine preference. H1 : There is no association between gender and magazine preference. 2. The degrees of freedom is 6. 3. The critical value at 10% is 4.61. 4. The test statistic calculated is 4.6924. 5. There is not enough evidence to reject the null hypothesis H0 at 10% of significance level. QUESTION 7 A local TV station claims that 60% of people support the candidate A, 30% support the candidate B, and 10% support the candidate C. A survey of 500 registered voters considered and the following table indicates how people were likely to vote. Candidate A Candidate B Candidate C 350 125 25 The analyst wants to test whether the TV station's claim can be rejected by the sample data. Which one of the following statements is correct? 1. The null hypothesis H0 : p1 = 0.10 p2 = 0.30 p3 = 0.30. 2. The alternative H1 : at least one p,- is equal to its specified value .0\" = 1, 2, 3). 3. The expected frequency for each candidate is 300, 150 and 50 respectively. 4. The rejection region at 5% level is 12
