# Indicate true or false for the following statements. If false, specify what change will make the statement true. a) In the two-sample t test, the numb

Indicate true or false for the following statements. If false, specify what change will make the statement true.
a) In the two-sample t test, the number of degrees of freedom for the test statistic increases as sample sizes increase.
b) When the means of two independent samples are used to to compare two population means, we are dealing with dependent (paired) samples.
c) The $$\displaystyle{x}^{{{2}}}$$ distribution is used for making inferences about two population variances.
d) The standard normal (z) score may be used for inferences concerning population proportions.
e) The F distribution is symmetric and has a mean of 0.
f) The pooled variance estimate is used when comparing means of two populations using independent samples.
g) It is not necessary to have equal sample sizes for the paired t test.

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Latisha Oneil

a) YES The number of df increases when sample size increases
$$\displaystyle{n}_{{1}}:\ {11},\ {n}_{{2}}:\ {12}$$
df: $$\displaystyle{n}_{{1}}\ +\ {n}_{{2}}\ -\ {2}$$
$$\displaystyle=\ {11}\ +\ {12}\ -\ {2}$$
$$\displaystyle=\ {21}$$
$$\displaystyle{n}_{{1}}\ =\ {13},\ {n}_{{2}}\ =\ {14}$$
df $$\displaystyle=\ {13}\ +\ {14}\ -{2}$$
$$\displaystyle=\ {27}\ -\ {2}$$
$$\displaystyle=\ {25}$$
b) NO Matched pains consint of two samples that are dependent.
$$\displaystyle{H}_{{0}}:\ \mu_{{d}}\ =\ {0}$$
There are the $$\mu_d:\ \mu_1-\mu_2\begin{cases}H_0: & \mu_d = 0\\A_0: & \mu_d \neq 0\end{cases}$$
c) NO. t-distribution is used for making infernces concening two population variance.(unequal variances)
d) YES for population proportion we are using
$$\displaystyle{z}\ -\ {d}{i}{s}{t}{r}{i}{b}{u}{t}{i}{o}{n}$$
$$\displaystyle{z}\ =\ {\frac{{\hat{{p}}\ -\ {p}}}{{\sqrt{{{P}{\left({1}\ -\ {p}\right)}}}{\left\lbrace{n}\right\rbrace}}}}$$
e) NO F distribution is not symmetric but it has mean of 0
f) YES when using independent samples to that the difference between two population means, pooled variance is used.
g) NO it is necesary to have equal sample sizes for the pained to test.