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The spread of the SARS-Cov-2 virus, beyond posing serious risks to physical health, also affected mental wellbeing. According to a release from the British Office of National Statistics in June2020, over two-thirds of adults reported feeling somewhat or very worried about the effect of COVID-19 on their life. From social isolation during lockdown, job loss, and housing security,there are several aspects of pandemic life that contributed to increased anxiety and distress.A study was conducted in New Zealand to examine the psychological health of New Zealanders during lockdown. Via an online survey during April 2020, the study team collected information on demographic variables and aspects of life during lockdown from 2,010 adults. For example, the survey included questions about alcohol consumption prior to lockdown and during lockdown, as well as whether the respondent felt satisfied with their quarantine bubble or that there had been some benefits of lockdown on a personal level (e.g., more time spent with family).The survey also included three standardized measures of psychological health: the Kessler Psychological Distress Scale (K10), the World Health Organization Well-Being Index (WHO-5), andthe Generalized Anxiety Disorder Screener (GAD-7).

– The primary outcome measure was K10 score. Scores on the K10 range from 0 to 40, with a higher score indicating a higher level of psychological distress. Respondents are asked to indicate how frequently over the past 4 weeks they have, for example, felt hopeless or depressed. Scores of 10-14 are classed as mild distress, scores of 15-19 as moderate distress,and scores of 20 or higher as severe distress. Scores of 12 or higher are considered indicative of an anxiety or depressive disorder.

– Scores on the WHO-5 range from 0 to 25, with a higher score indicating a higher level of psychological wellbeing. Respondents are asked to indicate frequently over the past 2 weeks they have, for example, felt cheerful and in good spirits, with higher frequency corresponding to a higher numerical score. Scores lower than 13 are indicative of low psychological wellbeing.

– Scores on the GAD-7 range from 0 to 21, with a higher score indicating a higher level of anxiety. Respondents are asked to indicate how frequently over the past 2 weeks they have,for example, felt unable to stop or control worrying, or felt that they have been worrying too much about different things.

Data from the study are in the filewellbeing.Rdata. The following table provides a list of the variables in the dataset and their descriptions.

The spread of the SARS-Cov-2 virus, beyond posing serious risks to physical health, also affected...

Use these data to answer the following questions.

a) (6 pts.) Describe the distribution of K10 score and K10 level for the study participants.Reference appropriate numerical and graphical summaries as needed. Additionally, report the proportion of patients with a score indicative of an anxiety or depressive disorder.

b) (8 pts.) A national survey from 2018 reported that the prevalence of adults in New Zealand experiencing low psychological well being (as characterized by a WHO-5 score lower than 13) was 25%. Conduct a formal analysis investigating whether these data indicate that the proportion of NZ adults experiencing low psychological wellbeing differs from 0.25; check any required assumptions. Summarize the findings, including reporting and interpreting an appropriate interval estimate.

c) (26 pts.) Researchers expected that elderly individuals would be more prone to experiencing poor mental health during lockdown than younger individuals, due to factors such as higher risk of social isolation and greater vulnerability to COVID-19.

i. The variableslives.alone,easy.contact, and loneliness provide some information about participants’ experience with social isolation. Investigate whether older individuals are more at risk of being socially isolated. Summarize the findings, referencing numerical results as necessary. Limit your answer to no more than ten sentences.

ii. Fit a model estimating the association between age and having K10 score higher than 11. In no more than four sentences, summarize the main finding(s) in language accessible to a general audience.

iii. Fit a model estimating the association between age and having K10 score higher than 11, adjusting for the three social isolation variables from in part i. Is this model or the analysis from part ii. preferable for understanding the association between age and having K10 score higher than 11? Explain your answer.

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