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The following is a set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution.
Test
H_(0):mu_(1)=mu_(2) vs
H_(a):mu_(1) > mu_(2) when the samples have
n_(1)=n_(2)=60,x_(1)=35.4,x_(2)=32.8,s_(1)=1.24, and
s_(2)=1.17. The standard error of
bar(x)_(1)- bar(x)_(2) from the randomization distribution is 0.22 .
Find the value of the standardized
z-test statistic.
Round your answer to two decimal places.

z=

The following is a set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution. $\newline$ Test $H_{0}: \mu_{1}=\mu_{2}$ vs $H_{a}: \mu_{1}>\mu_{2}$ when the samples have $n_{1}=n_{2}=60, x_{1}=35.4, x_{2}=32.8, s_{1}=1.24$ , and $s_{2}=1.17$ . The standard error of $\bar{x}_{1}-\bar{x}_{2}$ from the randomization distribution is $0$ . $22$ . $\newline$ Find the value of the standardized $z$ -test statistic. $\newline$ Round your answer to two decimal places. $\newline$ $z=$

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Find a value using two-variable equations: word problems

Full solution

Q. The following is a set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution.

\newline

Test

H_{0}: \mu_{1}=\mu_{2}

vs

H_{a}: \mu_{1}>\mu_{2}

when the samples have

n_{1}=n_{2}=60, x_{1}=35.4, x_{2}=32.8, s_{1}=1.24

, and

s_{2}=1.17

. The standard error of

\bar{x}_{1}-\bar{x}_{2}

from the randomization distribution is

0

.

22

.

\newline

Find the value of the standardized

z

-test statistic.

\newline

Round your answer to two decimal places.

\newline

z=

Identify means and error: Identify the sample means and standard error. $\bar{x}_1 = 35.4$ , $\bar{x}_2 = 32.8$ , and the standard error of the difference is $0.22$ .
Calculate mean difference: Calculate the difference between the sample means. $\newline$ Difference = $\bar{x}_1 - \bar{x}_2 = 35.4 - 32.8 = 2.6$ .
Compute z-test statistic: Compute the z-test statistic using the formula $z = (\text{Difference} - 0) / \text{SE}$ . $z = (2.6 - 0) / 0.22 = 11.82$ .

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