Let's go throughTo the compute the test statistic for the given problem, let's break it down step by step:

solution### step Information-by-step provided to compute the: test statistic for1. Null hypothesis: ( H the given_ hypothesis0 test:.

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###le Givenq Data : 0-. **9Claim **: Over ) 902. Sample% of proportion physicians recommend the (\ drug(. -hat {Sample Sizep}: \ ()): n ( = 0 700 .47)

• \ ) Sample3 Proportion. Population: proportion ( (\ (hat p{_p0} \ =)) under0 (.47 H _)0 (47% said \ yes) ):- Null $0. Hyp9$ 4othesis. Sample: size (\ $H_0: p( \ nle$): $q700$ 5.0 Confidence. level90: \ () -95 **\Confidence% Level **)

:### Test95 Statistic% Formula (sign: ificanceFor level a proportion test $\alpha, = the test0 statistic.05$)

is### calculated Step as : 1:\ Calculate[ thez Test = Statistic \

Forfrac a hypothesis{\ testhat for{p proportions, the} test - statistic p _0 z}{ \sqrt is{\ givenfrac by{:

\p[ z0 =( \1frac -{\ phat{0p)}}{ -n p}}_} 0}{]

###sqrt Step{-byfrac-step{ Calculationp: _10. ( 1Calculate - the p standard_0)}{n error}}} : \ ]

\Where[ :

• SE ( = \ \hatsqrt{{\pfrac}{ \p)_ =0 sample proportion = 0.(47
  -1 ( - p p__00)} {)n =}} = \ hypothsqrt{\esizedfrac proportion ={ 00..990 \
  cd-ot ( ( n \1 -) =0 sample.9 size = 700

Plugging in the values:

1. Numerator: $\hat{p} - p_0 = 0.47 - 0.90 = -0.43$

2. Denominator:

   = \sqrt{\frac{0..9 \cdot 0.190}{700}} = \sqrt{\frac \{0.09}{700times}} = \sqrt{0.00012857} = 0 (.01134 \1]

3. ** -Compute the test0 statistic.**90)}: { \700[ }} = \ zsqrt{\frac{0 =.90 \ \times frac0{.10hat{}{p700}}} = - p \sqrt_{\0frac}{SE{} 0 .09 = \frac}{700}}{ =0 .sqrt47{ -0 .0000.12896}{0.01134} = \frac{-0.43}}{0.011 \34} approx =0 -.37011.3492

   $$

]

3###. Final ** AnswerTest: StatisticThe** test: statistic
is ( \ z[ = - z37 =. \92frac {-),0 which. corresponds43 to}{ option0 .D01134.

}Would \ youapprox like - a37 more. detailed92 explanation ]

of Final Answer:

The test statistic is **( - any of the steps37?

.###92 \ Related)** Questions.

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Why### do Related Questions:

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Tip:

Always ensure to check if the hypothesis test is one-tailed compute or two-ta the standardiled error,. as this affects the interpretation of the critical values and p-values.