what is the a d polnn) Based on the simple egession moel above, of 30 mm Hg? b,
ID: 3326619 • Letter: W
Question
what is the a d polnn) Based on the simple egession moel above, of 30 mm Hg? b, (4 point) Calulate the approximate (assuming mean for an atmospherie pressure is 30 mmHg) 95% prediction interval for your estimate in part (a) above e) (4 points) Calculate the 95% confidence interval for by, the coefficient for pressure the variable atmospheric e) (4 points) Perform the appropriate hypothesis test to determine whether atmospheric pressure is a significant predictor of ozone concentration levels. Be sure to list the hypotheses in terms of parameters, the test statistic and degrees of freedom if applicable, the p-value, and whether or not you reject the null hypothesis.Explanation / Answer
a)
Based on the result provided,
The estimated ozone concentration level on a day
= 1095.183 + 7.571 * atmospheric pressure
Hence when the atmospheric pressure is 30 mmHg,
The estimated ozone concentration is equal to
1095.183 + 7.571 * 30
= 1322.313 in parts per 100 Million
b)
The 95% prediction interval of the ozone concentration when the atmospheric pressure is 30 mmHg is:
The lower 95 prediction interval is
= (1095.183 - 67.041) + (7.571 - 2.076) * 30
= 1192.992
The upper 95 prediction interval is
= (1095.183 + 67.041) + (7.571 + 2.076) * 30
= 1451.654
c)
95 confidence interval for the variable b1, the coefficient of atmospheric pressure is:
Lower 95 confidence interval is
= 7.571 - 2.076
= 5.495
Upper 95 confidence interval
= 7.571 + 2.076
= 9.647
d)
To determine whether the atmospheric pressure is a significant prediction of ozone concentration
Null hypothesis is: b1 (the coefficient of the variable atmospheric pressure) = 0
Alternate hypothesis is: b1 not equal to 0
The t statistic is = 7.571 / 2.076 = 3.647
The degrees of freedom for this t statistic = 1
So, the p-value of the hypothesis test is:
= 2 * P(T > 3.647 | T ~ t(1))
= 2 * (1 - pt(3.647,1))
= 0.1703
Which is greater than level of significance.
So we fail to reject the null hypothesis that b1 = 0
Hence we conclude that:
The atmospheric pressure is not a significant predictor of ozone concentration.
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