Respuesta :
Lower bound is : 2.70 and upper bound is 3.30
a)There is a 90% probability that the difference of the means is in the interval
b) Since the 90% confidence interval does not contain zero, the results suggest that priming does have an effect on scores.
What is Critical Value?
Critical values are essentially cut-off values that define regions where the test statistic is unlikely to lie; for example, a region where the critical value is exceeded with probability if the null hypothesis is true.
Given that:
a) [tex]n_1[/tex]=200, [tex]x_1[/tex]=23.9, [tex]s_1[/tex]=4.7
[tex]n_2[/tex]=200, [tex]x_2[/tex]=18.8, [tex]s_2[/tex]=4.5
The (1-α )% confidence interval for the difference between two mean is:
CI= [tex]x_1-x_2\pm\; t_\frac{\alpha }{2},(n_1+n_2-2\sqrt{\frac{s_1^{2}}{n_1}+\frac{s_2^{2}}{n_2} }[/tex]
the Critical value of 't' will be:
α/2=0.05/2=0.025
Degrees of freedom = [tex]n_1+n_2\\[/tex]-2= 200=200-2=398
[tex]t_{\alpha /2,_(n_1+n_2-2)}= t_{0.025,398}[/tex]=1.96
CI=23.9-18.8±1.96 [tex]\sqrt{\frac{4.7^{2}}{200}+\frac{4.5^{2}}{200} }[/tex]
= 3±0.3089
= (3.3089,2.6911)
≈(3.30, 2.70)
Thus, 90% confidence interval (3.30, 2.70) implies that the true mean difference value is contained in the interval with probability 0.90.
The Lower bound is : 2.70 and upper bound is 3.30
Thus, There is a 90% probability that the difference of the means is in the interval.
b)The difference between means, null value is 0.
As the null value is 0 and not in the interval, which shows that there is a difference between the two means, concluding that priming does have an effect on scores.
Hence, Since the 90% confidence interval does not contain zero, the results suggest that priming does have an effect on scores.
Learn more about this concept here:
https://brainly.com/question/16089384
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