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$Question 2 1pts You wish to test the following claim (H_(a)) at a significance level of alpha=0.05. {:[H_(o):p=0.42],[H_(a):p > 0.42]:} You obtain a sample of size n=143 in which there are 73 successful observations. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution. What is the critical value? Round to 2 decimal places. Question 3 1pts$

Question $2$ $\newline$ $1 \mathrm{pts}$ $\newline$ You wish to test the following claim $\left(\mathrm{H}_{\mathrm{a}}\right)$ at a significance level of $\alpha=0.05$ . $\newline$ $\begin{array}{l} \mathrm{H}_{\mathrm{o}}: p=0.42 \\ \mathrm{H}_{\mathrm{a}}: p>0.42 \end{array}$ $\newline$ You obtain a sample of size $n=143$ in which there are $73$ successful observations. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution. $\newline$ What is the critical value? Round to $2$ decimal places. $\newline$ Question $3$ $\newline$ $1 \mathrm{pts}$

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Math Problems

Grade 6

Solve one-step multiplication and division equations: word problems

Full solution

Q. Question

2

\newline

1 \mathrm{pts}

\newline

You wish to test the following claim

\left(\mathrm{H}_{\mathrm{a}}\right)

at a significance level of

\alpha=0.05

\newline

\begin{array}{l} \mathrm{H}_{\mathrm{o}}: p=0.42 \\ \mathrm{H}_{\mathrm{a}}: p>0.42 \end{array}

\newline

You obtain a sample of size

n=143

in which there are

73

successful observations. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.

\newline

What is the critical value? Round to

2

decimal places.

\newline

Question

3

\newline

1 \mathrm{pts}

Calculate Sample Proportion: Calculate the sample proportion $\hat{p}$ by dividing the number of successful observations by the sample size. $\hat{p} = \frac{73}{143}$
Find Standard Error: Find the standard error (SE) using the formula $SE = \sqrt{\left(p \times (1 - p)\right) / n}$ , where $p$ is the assumed population proportion under the null hypothesis. $\newline$ $SE = \sqrt{\left(0.42 \times (1 - 0.42)\right) / 143}$
Calculate Z-Score: Calculate the z-score for the sample proportion without the continuity correction using the formula $z = \frac{\hat{p} - p}{SE}$ . $\newline$ $z = \frac{\hat{p} - 0.42}{SE}$
Look Up Critical Value: Look up the critical z-value for a one-tailed test at $\alpha = 0.05$ using the standard normal distribution table or a calculator. $\newline$ The critical z-value is approximately $1.645$ .
Round Critical Value: Round the critical $z$ -value to two decimal places as instructed. $\newline$ Critical value = $1.65$