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A research is conducted to analyse whether the World Cup event has disturbance on the sleep quality of adults. A sample of 189 adults were interviewed. They were asked whether they watched soccer matches during 2022 World Cup tournament and examined whether they had symptoms of sleep deficiency. The table below shows number of adults in each category from the sample. Did you watch soccer matches during 2022 World Cup tournament? No 37 63 Are there any symptoms of sleep-deficiency? Yes Yes 50 39 No a) A researcher claims that for adults who did not watch soccer matches, the proportion of them having symptoms of sleep deficiency is different from 50%. Is there enough evidence to support the claim? Perform the hypothesis test using the P-value approach. b) Define Type I error in hypothesis test. What is the probability of Type I error in (a) if we decide to reject the null hypothesis? c) Suppose, for adults who watched soccer matches during the World Cup tournament, the proportion of them having symptoms of sleep deficiency is p₁, and for adults who did not watch soccer matches during the tournament, the proportion of them having the symptoms is P2. Is there enough evidence to conclude that adults who watched soccer matches during the World Cup tournament are more likely to have symptoms of sleep deficiency than those who did not watch soccer matches during the tournament, i.e, is p₁ > p₂? Perform the hypothesis test at the 1% significance level to justify your answer. d) Using the same notation as in (c), find the 95% confidence interval of P₁ - P2

A research is conducted to analyse whether the World Cup event has disturbance on the sleep quality of adults. A sample of 189 adults were interviewed. They were asked whether they watched soccer matches during 2022 World Cup tournament and examined whether they had symptoms of sleep deficiency. The table below shows number of adults in each category from the sample. Did you watch soccer matches during 2022 World Cup tournament? No 37 63 Are there any symptoms of sleep-deficiency? Yes Yes 50 39 No a) A researcher claims that for adults who did not watch soccer matches, the proportion of them having symptoms of sleep deficiency is different from 50%. Is there enough evidence to support the claim? Perform the hypothesis test using the P-value approach. b) Define Type I error in hypothesis test. What is the probability of Type I error in (a) if we decide to reject the null hypothesis? c) Suppose, for adults who watched soccer matches during the World Cup tournament, the proportion of them having symptoms of sleep deficiency is p₁, and for adults who did not watch soccer matches during the tournament, the proportion of them having the symptoms is P2. Is there enough evidence to conclude that adults who watched soccer matches during the World Cup tournament are more likely to have symptoms of sleep deficiency than those who did not watch soccer matches during the tournament, i.e, is p₁ > p₂? Perform the hypothesis test at the 1% significance level to justify your answer. d) Using the same notation as in (c), find the 95% confidence interval of P₁ - P2

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 27PPS
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May I know how to solve a) and c) ? Thank you.

A research is conducted to analyse whether the World Cup event has disturbance on the sleep quality of adults. A sample of 189 adults were interviewed. They were asked whether they watched soccer matches during 2022 World Cup tournament and examined whether they had symptoms of sleep deficiency. The table below shows number of adults in each category from the sample. Did you watch soccer matches during 2022 World Cup tournament? No 37 63 Are there any symptoms of sleep deficiency? Yes Yes 50 39 No a) A researcher claims that for adults who did not watch soccer matches, the proportion of them having symptoms of sleep deficiency is different from 50%. Is there enough evidence to support the claim? Perform the hypothesis test using the P-value approach. b) Define Type I error in hypothesis test. What is the probability of Type I error in (a) if we decide to reject the null hypothesis? c) Suppose, for adults who watched soccer matches during the World Cup tournament, the proportion of them having symptoms of sleep deficiency is p₁, and for adults who did not watch soccer matches during the tournament, the proportion of them having the symptoms is P2. Is there enough evidence to conclude that adults who watched soccer matches during the World Cup tournament are more likely to have symptoms of sleep deficiency than those who did not watch soccer matches during the tournament, i.e, is p₁ > P₂? Perform the hypothesis test at the 1% significance level to justify your answer. d) Using the same notation as in (c), find the 95% confidence interval of p₁ - P2
Transcribed Image Text:A research is conducted to analyse whether the World Cup event has disturbance on the sleep quality of adults. A sample of 189 adults were interviewed. They were asked whether they watched soccer matches during 2022 World Cup tournament and examined whether they had symptoms of sleep deficiency. The table below shows number of adults in each category from the sample. Did you watch soccer matches during 2022 World Cup tournament? No 37 63 Are there any symptoms of sleep deficiency? Yes Yes 50 39 No a) A researcher claims that for adults who did not watch soccer matches, the proportion of them having symptoms of sleep deficiency is different from 50%. Is there enough evidence to support the claim? Perform the hypothesis test using the P-value approach. b) Define Type I error in hypothesis test. What is the probability of Type I error in (a) if we decide to reject the null hypothesis? c) Suppose, for adults who watched soccer matches during the World Cup tournament, the proportion of them having symptoms of sleep deficiency is p₁, and for adults who did not watch soccer matches during the tournament, the proportion of them having the symptoms is P2. Is there enough evidence to conclude that adults who watched soccer matches during the World Cup tournament are more likely to have symptoms of sleep deficiency than those who did not watch soccer matches during the tournament, i.e, is p₁ > P₂? Perform the hypothesis test at the 1% significance level to justify your answer. d) Using the same notation as in (c), find the 95% confidence interval of p₁ - P2
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