Write the claim mathematically and Identify H_0 and H_a. Find the critical value

Question

Write the claim mathematically and Identify H_0 and H_a. Find the critical value(s) and identify the rejection region(s). Find the standardized test statistic. Decide whether to reject or fail to reject the null hypothesis. A medical researcher says that at least 23% of adults are smokers. In a sample of 250 adults, 22.8% say they are smokers. At alpha = 0.04, do you have enough evidence to reject the researcher's claim? (a) Which of the following correctly states H_0 and H_a? A. H_0: p = 0.23 H_a: p > 0.23 B. H_0 p > 0.23 H_a: p lessthanorequalto 0.23 C. H_0 p

Explanation / Answer

The statistical software output for this problem is:

One sample proportion summary hypothesis test:
p : Proportion of successes
H0 : p = 0.23
HA : p < 0.23

Hypothesis test results:

Hence,

Critical value = -1.75

Test statistic = -0.08

Do not reject Ho.

Proportion Count Total Sample Prop. Std. Err. Z-Stat P-value p 57 250 0.228 0.026615785 -0.075143379 0.4701

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