In a city, according to a 1990 demographic report based on the census result, the average daily spending on food per person is $75. In 2020, a random sample of 28 persons in the same city is selected and the daily spending ($) on food for each interviewee is recorded as follow: 55.0 59.5 62.5 65.5 68.5 69.0 70.0 70.0 82.0 82.5 83.5 85.0 86.0 86.5 86.5 87.0 87.0 87.0 89.0 92.5 93.0 94.5 94.5 96.0 98.0 102.5 108.5 110.5 (a) Find the point estimate for the population mean daily spending on food per person in year 2020. (b) It is assumed that the spending is normally distributed. Construct a 90% confidence interval estimate for the population mean daily spending on food per person in year 2020. (c) Is there sufficient evidence to conclude that the population mean daily spending on food per person in 2020 is higher than 1990? Test at 1% level of significance. (State clearly the null hypothesis, alternatively hypothesis, rejection region, test statistics and conclusion.)

In a city, according to a 1990 demographic report based on the census result, the average daily spending on
food per person is $75.
In 2020, a random sample of 28 persons in the same city is selected and the daily spending ($) on food for
each interviewee is recorded as follow:
55.0 59.5 62.5 65.5 68.5 69.0 70.0 70.0 82.0 82.5
83.5 85.0 86.0 86.5 86.5 87.0 87.0 87.0 89.0 92.5
93.0 94.5 94.5 96.0 98.0 102.5 108.5 110.5
(a) Find the point estimate for the population mean daily spending on food per person in year 2020.
(b) It is assumed that the spending is normally distributed. Construct a 90% confidence interval estimate
for the population mean daily spending on food per person in year 2020.
(c) Is there sufficient evidence to conclude that the population mean daily spending on food per person in
2020 is higher than 1990? Test at 1% level of significance. (State clearly the null hypothesis,
alternatively hypothesis, rejection region, test statistics and conclusion.)

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