Exam 12: Tests With Qualitative Data

The number of visits to a certain web site were counted each day of a particular week. The results are given in the following table. Day Number of Visits Sunday 134 Monday 111 Tuesday 125 Wednesday 123 Thursday 122 Friday 150 Saturday 150 Test the hypothesis that web site visits are equally likely to occur on any day of the week. Use the $\alpha$ = 0.05 Level of significance.

A biology professor claims that, on the average, 20% of her students get a grade of A, 30% get a B, 35% get a C, 10% get a D, and 5% get an F. The grades of a random sample of 137 students were recorded. The following table presents the results. Grade 1 2 3 4 5 Observed 27 37 52 16 5 i). Compute the expected frequencies. ii). What is the value of $\chi ^ { 2 }$ ? iii). How many degrees of freedom are there? iv). Test the hypothesis that the grades follow the distribution claimed by the professor. Use the $\alpha$ = 0.05 level of significance.

The following table presents the numbers of cucumber seeds, by brand, that germinated or failed to germinate 14 days after planting. Brand A Brand B Brand C Brand D Germinated 44 33 35 31 Failed to Germinate 10 9 2 17 Can you conclude that the germination rate is related to the brand of seed? Use the $\alpha = 0.01$ level of Significance.

A sample of 178 university students who recently moved off-campus were polled to see whether they agree that off-campus living is preferable to on-campus living. In addition, each was asked how many people live in their current off-campus residence. The results are summarized in the following contingency table. 1 2 3 Agree 36 41 26 No Opinion 7 7 30 Disagree 2 10 19 i). Compute the row totals, the column totals, and the grand total. ii). Construct the corresponding table of expected values. iii). Compute the value of the chi-square test statistic. iv). Perform a test for independence, using the $\alpha = 0.01$ level of significance. What do you conclude?

Following are observed frequencies. The null hypothesis is $H _ { 0 } : p _ { 1 } = 0.35 , p _ { 2 } = 0.2 , p _ { 3 } = 0.15$ , $p _ { 4 } = 0.15 , p _ { 5 } = 0.15$ . Category 1 2 3 4 5 Observed 32 37 7 23 4 Compute the value of $\chi ^ { 2 }$ .

Following is a set of observed and expected frequencies: Observed 10 20 26 30 19 Expected 10 10 20 20 15 Test the hypothesis that the distribution of the observed frequencies is as given by the expected frequ Use the $\alpha = 0.01$ level of significance.

A psychology instructor gave a five-question true-false quiz to her class of 201 students. The results were as follows. Number Correct 0 1 2 3 4 5 Observed 10 40 56 64 25 6 The instructor thinks that the students may have answered the questions by guessing, so that the probability that Any given answer is correct is 0.5. Under the null hypothesis, the number of correct answers has a binomial Distribution with 5 trials and success probability 0.5. Perform a chi-square test of this hypothesis. Can you reject H₀ at the $\alpha$ =0.01 level?

For the following observed and expected frequencies, compute the value of $\chi ^ { 2 }$ Observed 8 12 29 7 18 Expected 10 15 30 15 15

A biology professor claims that, on the average, 10% of her students get a grade of A, 30% get a B, 35% get a C, 10% get a D, and 15% get an F. The grades of a random sample of 113 students were Recorded. The following table presents the results. Grade 1 2 3 4 5 Observed 3 34 38 12 26 Compute the expected frequencies.

Following are observed frequencies. The null hypothesis is H₀: p₁=0.35, p₂=0.3, p₃=0.1,p₄=0.15, p₅=0.1 Category 1 2 3 4 5 Observed 51 32 11 13 16 Test the hypothesis that the distribution of the observed frequencies is as given by the null hypothesis $\alpha = 0.01$ level of significance.

A sample of 149 university students who recently moved off-campus were polled to see whether they agree that off-campus living is preferable to on-campus living. In addition, each was asked how many people live in Their current off-campus residence. The results are summarized in the following contingency table. 1 2 3 Agree 25 17 34 No Opinion 8 12 15 Disagree 11 18 6 Perform a test for independence, using the $\alpha = 0.01$ level of significance. What do you conclude?

Following are observed frequencies. The null hypothesis is H₀: p₁=0.4, p₂=0.2, p3=0.15,p₄=0.1, p₅=0.15 Category 1 2 3 4 5 Observed 38 26 18 4 13 Compute the expected frequencies.

The number of drunk-driving arrests were counted each month by the Millville police department. The results are given in the following table. Month Number of Drunk-Driving Arrests January 24 February 21 March 13 April 11 May 13 June 11 July 10 August 13 September 14 October 14 November 13 December 25 Test the hypothesis that drunk-driving arrests are equally likely to occur in any month. Use the $a$ = 0.05 level Of significance.

The following table presents the numbers of cucumber seeds, by brand, that germinated or failed to germinate 14 days after planting. Brand A Brand B Brand C Brand D Germinated 34 31 37 29 Failed to Germinate 6 2 5 13 Can you conclude that the germination rate is related to the brand of seed? Use the $\alpha = 0.05$ level of significance.

The following table presents the numbers of customers who - after 2 weeks of use - were satisfied or dissatisfied with their newly-purchased computers. Brand A Brand B Brand C Brand D Satisfied 38 26 21 44 Dissatisfied 3 9 13 9 Can you conclude that the satisfaction rate is related to the brand of computer? Use the $\alpha = 0.05$ level of Significance.

The following table presents the numbers of customers who - after 2 weeks of use - were satisfied or dissatisfied with their newly-purchased computers. Brand A Brand B Brand C Brand D Satisfied 35 31 47 33 Dissatisfied 14 15 5 3 Can you conclude that the satisfaction rate is related to the brand of computer? Use the $\alpha = 0.01$ level of significance.

The number of drunk-driving arrests were counted each month by the Millville police department. The results are given in the following table. Month Number of Drunk-Driving Arrests January 24 February 19 March 22 April 13 May 12 June 11 July 10 August 12 September 10 October 10 November 15 December 26 Test the hypothesis that drunk-driving arrests are equally likely to occur in any month. Use the $\alpha$ = 0.05 level of significance.

A biology professor claims that, on the average, 15% of her students get a grade of A, 30% get a B, 30% get a C, 10% get a D, and 15% get an F. The grades of a random sample of 105 students were Recorded. The following table presents the results. Grade 1 2 3 4 5 Observed 17 39 26 5 18 Test the hypothesis that the grades follow the distribution claimed by the professor. Use the $\alpha = 0.01$ level of Significance.

A biology professor claims that, on the average, 15% of her students get a grade of A, 20% get a B, 40% get a C, 15% get a D, and 10% get an F. The grades of a random sample of 135 students were Recorded. The following table presents the results. Grade 1 2 3 4 5 Observed 14 13 48 43 17 What is the value of $\chi ^ { 2 }$ ?

Following are observed frequencies. The null hypothesis is H₀: p₁=0.3, p₂=0.2, p₃=0.2, p₄=0.15, p₅=0.15 . Category 1 2 3 4 5 Observed 38 26 18 4 13 i). Compute the expected frequencies. ii). Compute the value of X². iii). How many degrees of freedom are there? iv). Test the hypothesis that the distribution of the observed frequencies is as given by the null hypot] the $\alpha$ =0.01 level of significance.