Question

According to the previous census, the mean income of all part-time working students was $400/per week with a standard deviation of $100. A report published recently claims that post-Covid19, the mean income of all part-time working students has increased. To test the claims of the report, a survey was conducted among 400 part-time working students. Let X denote the mean of a random sample of size n = 400. Our decision is to reject H0 when X > $409.87. a) Write down the null and alternative hypotheses. (0.5 marks) H0: HA: b) Choose a significance level and explain its relevance in the context of Type I Error. (0.5 marks) c) If the value of X computed from the data is X = $450 per week, calculate Zstat (3 marks) d) Write down the decision rule based on the p-value = 0.00001 (0.5 marks) e) If we retain H0 when ? = $420, what type of error did we make? (0.5 marks) Type I Type II (circle one) Explain your response.

          According to the previous census, the mean income of all part-time working students was $400/per week with a standard deviation of $100. A report published recently claims that post-Covid19, the mean income of all part-time working students has increased. To test the claims of the report, a survey was conducted among 400 part-time working students. Let X denote the mean of a random sample of size n = 400. Our decision is to reject H0 when X > $409.87.

a) Write down the null and alternative hypotheses. (0.5 marks)
H0:
HA:

b) Choose a significance level and explain its relevance in the context of Type I Error. (0.5 marks)

c) If the value of X computed from the data is X = $450 per week, calculate Zstat (3 marks)

d) Write down the decision rule based on the p-value = 0.00001 (0.5 marks)

e) If we retain H0 when ? = $420, what type of error did we make? (0.5 marks)
Type I Type II (circle one)
Explain your response.

According to the previous census, the mean income of all part-time working students was 400/per week with a standard deviation of100. A report published recently claims that post-Covid19, the mean income of all part-time working students has increased. To test the claims of the report, a survey was conducted among 400 part-time working students. Let X denote the mean of a random sample of size n = 400. Our decision is to reject H0 when X > 409.87.

a) Write down the null and alternative hypotheses. (0.5 marks)
H0:
HA:

b) Choose a significance level and explain its relevance in the context of Type I Error. (0.5 marks)

c) If the value of X computed from the data is X =450 per week, calculate Zstat (3 marks)

d) Write down the decision rule based on the p-value = 0.00001 (0.5 marks)

e) If we retain H0 when ? = 420, what type of error did we make? (0.5 marks)
Type I Type II (circle one)
Explain your response.

Added by Jennifer M.

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