Question

A psychologist who needs two groups of students for a learning experiment decides to select a random sample of 110 female college students and 73 male college students. Before the experiment, the psychologist administers an IQ test to both groups to determine if there is a significant difference in their mean IQ scores. The population standard deviation for this IQ test is know to be 13 for both female and male populations. If the sample mean IQ score of the 110 female students is 118.6 and the sample mean IQ score for the 73 male students is 120, can the psychologist conclude that there is a significant difference in the mean IQ score of both groups at $\alpha = 5\%$? Let population 1 be female students and population 2 be male students. Note that direction is not specified in this problem, and the population standard deviation is given. See Chapter 13. (a) State the hypotheses: $H_0$: The population mean IQ score for female students is equal to the population mean IQ score for male students. Symbols: $\mu_1 \mu_2 \mu_{\bar{x}_1 - \bar{x}_2} \mu_\bar{p} \mu_1 - \mu_2 \p_1 \p_2 \bar{p} \mu \p = 0$ $H_a$: The population mean IQ score for female students is not equal to the population mean IQ score for male students. Symbols: $\mu_1 \mu_2 \mu_{\bar{x}_1 - \bar{x}_2} \mu_\bar{p} \mu_1 - \mu_2 \p_1 \p_2 \bar{p} \mu \p = 0$ (b) The correct symbol for the mean of the sampling distribution is: $\bar{r} \bar{x} \frac{x^2}{p_1 - p_2} \frac{\bar{x}_1 - \bar{x}_2}{p} \mu \p_1 - p_2 \bar{x}_1 - \bar{x}_2$ (c) The value for the mean of the sampling distribution is: 0 (d) Choose the correct distribution: Chi-Square Distribution Normal Distribution Why? T-Distribution The size of $n_1 < 30$ and $n_2 < 30$. $n_1p_1$, $n_1(1-p_1)$, $n_2p_2$, and $n_2(1-p_2)$ are all greater than 5. We are provided with $\bar{x}_1$ and $\bar{x}_2$. We are not provided with $\sigma$ for the two populations. The size of $n_1 > 30$ and $n_2 > 30$. We are provided with $\sigma$ for the two populations. (e) State the decision rule: Reject $H_0$ and accept $H_a$ at $\alpha = 5\%$ is less than or equal to 0.05 (f) Experiment: Symbol of the sample statistic: $\mu_{\bar{p}} \bar{x}_1 - \bar{x}_2 \bar{p} \mu_{\bar{x}} \p_1 - p_2 \mu_{\bar{x}_1 - \bar{x}_2} \p \bar{x}_2 - \bar{x}_1 \mu$ $\x^2 \mu_2$ Value of the sample statistic rounded to 1 decimal place: P-value of the sample statistic rounded to 4 decimal places:

          A psychologist who needs two groups of students for a learning experiment decides to select a random
sample of 110 female college students and 73 male college students. Before the experiment, the
psychologist administers an IQ test to both groups to determine if there is a significant difference in their
mean IQ scores. The population standard deviation for this IQ test is know to be 13 for both female and
male populations. If the sample mean IQ score of the 110 female students is 118.6 and the sample mean IQ
score for the 73 male students is 120, can the psychologist conclude that there is a significant difference in
the mean IQ score of both groups at $\alpha = 5\%$? Let population 1 be female students and population 2 be male
students.
Note that direction is not specified in this problem, and the population standard deviation is given. See
Chapter 13.
(a) State the hypotheses:
$H_0$: The population mean IQ score for female students is equal to the
population mean IQ score for male students.
Symbols: $\mu_1 \mu_2 \mu_{\bar{x}_1 - \bar{x}_2} \mu_\bar{p} \mu_1 - \mu_2 \p_1 \p_2 \bar{p} \mu \p = 0$
$H_a$: The population mean IQ score for female students is not equal to the
population mean IQ score for male students.
Symbols: $\mu_1 \mu_2 \mu_{\bar{x}_1 - \bar{x}_2} \mu_\bar{p} \mu_1 - \mu_2 \p_1 \p_2 \bar{p} \mu \p = 0$
(b) The correct symbol for the mean of the sampling distribution is:
$\bar{r} \bar{x} \frac{x^2}{p_1 - p_2} \frac{\bar{x}_1 - \bar{x}_2}{p} \mu \p_1 - p_2 \bar{x}_1 - \bar{x}_2$
(c) The value for the mean of the sampling distribution is: 0
(d) Choose the correct distribution:
Chi-Square Distribution
Normal Distribution
Why?
T-Distribution
The size of $n_1 < 30$ and $n_2 < 30$.
$n_1p_1$, $n_1(1-p_1)$, $n_2p_2$, and $n_2(1-p_2)$ are all greater than 5.
We are provided with $\bar{x}_1$ and $\bar{x}_2$.
We are not provided with $\sigma$ for the two populations.
The size of $n_1 > 30$ and $n_2 > 30$.
We are provided with $\sigma$ for the two populations.
(e) State the decision rule:
Reject $H_0$ and accept $H_a$ at $\alpha = 5\%$
is less than or equal to 0.05
(f) Experiment:
Symbol of the sample statistic:
$\mu_{\bar{p}} \bar{x}_1 - \bar{x}_2 \bar{p} \mu_{\bar{x}} \p_1 - p_2 \mu_{\bar{x}_1 - \bar{x}_2} \p \bar{x}_2 - \bar{x}_1 \mu$
$\x^2 \mu_2$
Value of the sample statistic rounded to 1 decimal place:
P-value of the sample statistic rounded to 4 decimal places:

A psychologist who needs two groups of students for a learning experiment decides to select a random
sample of 110 female college students and 73 male college students. Before the experiment, the
psychologist administers an IQ test to both groups to determine if there is a significant difference in their
mean IQ scores. The population standard deviation for this IQ test is know to be 13 for both female and
male populations. If the sample mean IQ score of the 110 female students is 118.6 and the sample mean IQ
score for the 73 male students is 120, can the psychologist conclude that there is a significant difference in
the mean IQ score of both groups at α = 5%? Let population 1 be female students and population 2 be male
students.
Note that direction is not specified in this problem, and the population standard deviation is given. See
Chapter 13.
(a) State the hypotheses:
H0: The population mean IQ score for female students is equal to the
population mean IQ score for male students.
Symbols: μ1 μ2 μx̅1 - x̅2μp̅μ1 - μ2 1 2 p̅μ = 0
Ha: The population mean IQ score for female students is not equal to the
population mean IQ score for male students.
Symbols: μ1 μ2 μx̅1 - x̅2μp̅μ1 - μ2 1 2 p̅μ = 0
(b) The correct symbol for the mean of the sampling distribution is:
r̅x̅(x^2)/(p1 - p2)(x̅1 - x̅2)/(p)μ1 - p2 x̅1 - x̅2
(c) The value for the mean of the sampling distribution is: 0
(d) Choose the correct distribution:
Chi-Square Distribution
Normal Distribution
Why?
T-Distribution
The size of n1 < 30 and n2 < 30.
n1p1, n1(1-p1), n2p2, and n2(1-p2) are all greater than 5.
We are provided with x̅1 and x̅2.
We are not provided with σ for the two populations.
The size of n1 > 30 and n2 > 30.
We are provided with σ for the two populations.
(e) State the decision rule:
Reject H0 and accept Ha at α = 5%
is less than or equal to 0.05
(f) Experiment:
Symbol of the sample statistic:
μp̅x̅1 - x̅2 p̅μx̅1 - p2 μx̅1 - x̅2x̅2 - x̅1 μ
^2 μ2
Value of the sample statistic rounded to 1 decimal place:
P-value of the sample statistic rounded to 4 decimal places:

Added by Rosario W.

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