Complete Question
A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 40 girls and 40 boys in a community and gave them the standard memory test. The mean score for girls was 68 and the standard deviation of mean was 5.0. The mean score for boys was 66 and the standard deviation of mean was 5.0. What is the p-value and your conclusion at alpha 0.05
Answer:
The p-value is [tex]p-value =0.073614[/tex]
The conclusion is
There is sufficient evidence to support the claim that there was no significant difference between boys and girls on a standard memory test
Step-by-step explanation:
From the question we are told that
The sample size of boys and girls is [tex]n_1= n_2 = n = 40[/tex]
The standard deviation is [tex]s_1= s_2 = s = 5[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The sample mean for boys is [tex]\= x_1 =66[/tex]
The null hypothesis is [tex]H_o : \mu_1 = \mu_2[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 < \mu_2[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\= x_1 - \= x_2 }{ \sqrt{\frac{s_1 ^2 }{n_1} + \frac{s_2 ^2 }{n_1} } }[/tex]
=> [tex]z = \frac{66 -68 }{ \sqrt{\frac{5^2 }{40} + \frac{5 ^2 }{40} } }[/tex]
=> [tex]z = -1.789[/tex]
From the z table the area under the normal curve to the left corresponding to -1,789 is
[tex]P(Z < -.1789 ) = 0.036807[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = 2 P(Z < -.1789 )[/tex]
=> [tex]p-value = 2 * 0.036807[/tex]
=> [tex]p-value =0.073614[/tex]
From the values obtained we see that [tex]p-value < \alpha[/tex] hence
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is sufficient evidence to support the claim that there was no significant difference between boys and girls on a standard memory test
