# Question 4. Marketing professors at Robert Morris and Kent Sate universities examined children's recall and recognition of television advertisements. Two groups of children were shown a 60-second commercial for Sunkist Fun Fruit Rock-n-Roll Shapes. One group (the A/V group) was shown the ad with both audio and video; the second group (the video-only group) was shown only the video portion of the commercial. Following the viewing, the children were asked to recall 10 specific items from the ad. The number of the 10 items recorded correctly by each child is summarized in the table. The researchers theorized that "children who receive an audiovisual presentation will have the same level of mean recall of ad information as those who receive only the visual aspects of the ad". Video Only Group A/V Group n = 20 X = 3.70 si = 1.98 n2 = 20 X = 3.30 S2 = 2.13 a. Set up the appropriate null and alternative hypothesis to test the researchers' theory. b. Find the value of the test statistic. C. Give the rejection region for a = .10. d. Make the appropriate inference. What can you say about the researchers' theory? e. The researchers reported the p-value of the test as p-value=.542. Interpret the result. f. What conditions are required for the inference to be valid?

UGIGLE The Asker · Probability and Statistics

Transcribed Image Text: 4. Marketing professors at Robert Morris and Kent Sate universities examined children's recall and recognition of television advertisements. Two groups of children were shown a 60-second commercial for Sunkist Fun Fruit Rock-n-Roll Shapes. One group (the A/V group) was shown the ad with both audio and video; the second group (the video-only group) was shown only the video portion of the commercial. Following the viewing, the children were asked to recall 10 specific items from the ad. The number of the 10 items recorded correctly by each child is summarized in the table. The researchers theorized that "children who receive an audiovisual presentation will have the same level of mean recall of ad information as those who receive only the visual aspects of the ad". Video Only Group A/V Group n = 20 X = 3.70 si = 1.98 n2 = 20 X = 3.30 S2 = 2.13 a. Set up the appropriate null and alternative hypothesis to test the researchers' theory. b. Find the value of the test statistic. C. Give the rejection region for a = .10. d. Make the appropriate inference. What can you say about the researchers' theory? e. The researchers reported the p-value of the test as p-value=.542. Interpret the result. f. What conditions are required for the inference to be valid?
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Transcribed Image Text: 4. Marketing professors at Robert Morris and Kent Sate universities examined children's recall and recognition of television advertisements. Two groups of children were shown a 60-second commercial for Sunkist Fun Fruit Rock-n-Roll Shapes. One group (the A/V group) was shown the ad with both audio and video; the second group (the video-only group) was shown only the video portion of the commercial. Following the viewing, the children were asked to recall 10 specific items from the ad. The number of the 10 items recorded correctly by each child is summarized in the table. The researchers theorized that "children who receive an audiovisual presentation will have the same level of mean recall of ad information as those who receive only the visual aspects of the ad". Video Only Group A/V Group n = 20 X = 3.70 si = 1.98 n2 = 20 X = 3.30 S2 = 2.13 a. Set up the appropriate null and alternative hypothesis to test the researchers' theory. b. Find the value of the test statistic. C. Give the rejection region for a = .10. d. Make the appropriate inference. What can you say about the researchers' theory? e. The researchers reported the p-value of the test as p-value=.542. Interpret the result. f. What conditions are required for the inference to be valid?
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Solution:(a) Null hypothesis: There is no signiticant difference between the childuen who receive an audio visual presentation and those children who receive only the visual aspected of the advertisement with regard to the level of recall ofi.e, H_(0):u_(1)-u_(2)=0Alternative Hypothesis: Tneue is significant difference between the children who receive an audio vorual puesentation and thase children who receive only the visual aspat of the advertisement.i.e, H_(1):(u_(1)-u_(2))!=0(b) Given bar(x)_(1)=3.70 and bar(x)_(2)=3.30*s_(1)^(2)=(1.98)^(2),s_(2)^(2)=(2.13)^(2) under H_(0), the test statistic is:{:[t=(( bar(x)_(1)- bar(x)_(2)))/(sqrt(((s_(1)^(2))/(n_(1)))+((s_(2)^(2))/(n_(2)))))-t_(n_(1)+n_(2)-2)],[=(3.7-3.3)/(sqrt(((1.98)^(2))/(20))+(((2-13)^(2))/(20))))=0.6151]:}(c) The rejection region:|t| > t_(alpha//2)i.e. t < - ... See the full answer