Adele read a report saying that 49\%49%49, percent of teachers in the United States were members of a labor union. She wanted to test whether this was true in her state, so she took a random sample of 300300300 teachers from her state to test H_0:p=0.49H 0
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:p=0.49H, start subscript, 0, end subscript, colon, p, equals, 0, point, 49 versus H_\text{a}:p \neq 0.49H
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=0.49H, start subscript, start text, a, end text, end subscript, colon, p, does not equal, 0, point, 49, where ppp is the proportion of teachers in her state who are members of a labor union.
Adele found that 44\%44%44, percent of teachers in the sample were members of a labor union. She calculated a test statistic of z \approx -1.73z≈−1.73z, approximately equals, minus, 1, point, 73 a P-value of approximately 0.0830.0830, point, 083 for these results. Assume that the conditions for inference were met.
Is there sufficient evidence at the \alpha=0.05α=0.05alpha, equals, 0, point, 05 level to conclude that the proportion of teachers in her state that are members of a labor union is different than 49\%49%49, percent?