A scientist estimates that the mean nitrogen dioxide level in a city is greater

Question

A scientist estimates that the mean nitrogen dioxide level in a city is greater than 33 parts per billion. To test this estimate, you determine the nitrogen dioxide levels for 31 randomly selected days. The results (in parts per billion) are listed to the right. Assume that the population standard deviation is 11. At = 0.03, can you support the scientist's estimate? Complete parts (a) through (e) 27 39 37 42 29 20 3122 24 28 30 26 35 41 41 16 31 20 34 42 35 16 30 40 33 21 34 28 1535 32 (a) Write the claim mathematically and identify Ho and Ha Choose from the following 0 A. HOP 233 (claim) D. HOP 33 OB, Ho : 33 (claim) OF. Ho H 33 (claim) Ha : 33 (claim) Ha : > 33 (b) Find the critical value and identify the rejection region L (Round to two decimal places as needed.) Rejection region zLM (c) Find the standardized test statistic. z=| | (Round to two decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis O Fail to reject Ho O Reject Ho (e) Interpret the decision in the context of the original claim At the 3% significance level, there enough evidence to | the scientist's claim that the mean nitrogen dioxide level in the city is greater than 33 parts per billion

Explanation / Answer

The statistical software output for this problem is:

One sample Z hypothesis test:
: Mean of variable
H0 : = 33
HA : > 33
Standard deviation = 11

Hypothesis test results:

Hence,

a) Hypotheses: Option D is correct.

b) z0 = 1.88

Rejection region: z > 1.88

c) z = -1.45

d) Fail to reject Ho

e) is not; support

Variable n Sample Mean Std. Err. Z-Stat P-value Data 31 30.129032 1.9756583 -1.4531702 0.9269

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