This question is incomplete, the complete question is;
4. A scale measuring trust inthe media was administered to a random sample of 114 Democrats and 112 Republicans. The researcher finds that Democrats average a score of 8.5 on this scale, while Republicans average a score of 7.8. Together the Democrats and Republicans have a pooled standard error of .32. Is there a statistically significant difference between Democrats and Republicans in their level of trust in the media (at the alpha = .05 level )
Answer:
p-value 0.0297
Hence, p value ( 0.0297 ) is LESS THAN ∝ ( 0.05 )
Therefore, this is sufficient evidence to conclude that there is difference between Democrats and Republicans in their level of trust in the media.
Step-by-step explanation:
Given the data in the question;
H₀ : u₁ = u₂
Hₐ : u₁ ≠ u²
test statistics
t = x - u / s
we substitute
t = ( 8.5 - 7.8 ) / 0.32
t = 0.7 / 0.32
t = 2.1875
∝ = 0.05
degree of freedom = n₁ + n₂ - 2 = 114 + 112 - 2 = 224
so
{t[tex]_{\alpha /2[/tex], [tex]_{df[/tex] } = {t[tex]_{0.025[/tex], [tex]_{224[/tex] } = 1971
p-value = 0.02974
p-value 0.0297
Hence, p value ( 0.0297 ) is LESS THAN ∝ ( 0.05 )
Therefore, this is sufficient evidence to conclude that there is difference between Democrats and Republicans in their level of trust in the media.
