The FloridaLakes dataset describes characteristic of water samples taken at at r

Question

The FloridaLakes dataset describes characteristic of water samples taken at at random Florida lakes. Acidity given for each lake. Pure water has a pH of 7, which is neutral. Solutions with a pH less than 7 are acidic while solutions with a pH greater than 7 are basic or alkaline. The researchers would like to know whether on average the solutions in Florida lakes are acidic. (1) (2 points) The output of a certain step in the statistical analysis is given below. What are the name and purpose of this test? Shapiro-Wilk W test for normal data Variable Obs Prob z 0.881. 0.98211 0.272 0.60706 53 (2) (2 points) What is the conclusion of the test above? Why? How does the conclusion affect the one sample T procedure? one-sample t test Obs Std Err Std. Dev. [99% Conf Interval Variable Mean 53 6.590566 1769821 1.288449 6.117363 7.063769 mean mean (ph) t 2.3134 Ho mean 7 degrees of freedom 52 Ha mean, 7 Ha mean 7 Ha mean 7 Pr (T K t) 0.0123 Pr (ITI It 0.0247 Pr (T t) 0.9877

Explanation / Answer

1. H0: the data follows normal distribution

H1; the data not follows normal distribution

For testing normality, we use Shiprov- wilk test,

From the output, the p-value = 0.60706 which is > alpha 0.05, so we accept H0

Thus we conclude that the data follows normal distribution

2. Since the give data is normal, so we can use t-tet on this data.

3. sample size n = 53

4. point estimate of the population mean = 6.590566

5. The confidence inerval is (6.117363 and 7.063769)

99% chance that the population mean would be 6.117363 and 7.063769

6. H0 : The average solution is florida lakes are not acidic i.e. H0: mu = 7

H1: The average solution is florida lakes are acidic i.e. H0: mu < 7

7. Test statistic t =( 6.590566-7) / 0.1769821 =2.3134

8. P-value = 0.0123

9. Here P-value > alpha 0.01, we accept H0

Thus we conclude that The average solution is florida lakes are not acidic i.e. H0: mu = 7

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