Seorang manager produksi menyatakan bahwa isi sebuah susu kaleng sekurang -kurangnya 31 ons. Jika pengambilan sampel secara acak 60 kaleng susu diperoleh isi rata-rata 31,98 ons dan standar deviasi sampel adalah Tons perlukan kita meyakini pernyataan manager produksi tersebut? Berdasarkan deskripsi di atas rumusan hipotesis yang tepat adalah __ Select one: H_(0):mu =31 H_(1):mu gt 31 H_(0):mu leqslant 31 H_(1):mu gt 31 H_(0):mu geqslant 31 H_(1):mu lt 31 H_(0):mu =31 H_(1):mu neq 31

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Seorang manager produksi menyatakan bahwa isi sebuah susu kaleng sekurang -kurangnya 31 ons. Jika pengambilan sampel secara acak 60 kaleng susu diperoleh isi rata-rata 31,98 ons dan standar deviasi sampel adalah Tons perlukan kita meyakini pernyataan manager produksi tersebut? Berdasarkan deskripsi di atas rumusan hipotesis yang tepat adalah __ Select one: H_(0):mu =31 H_(1):mu gt 31 H_(0):mu leqslant 31 H_(1):mu gt 31 H_(0):mu geqslant 31 H_(1):mu lt 31 H_(0):mu =31 H_(1):mu neq 31

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Answer 1

B. \(H_{0}: \mu \leq 31\) \\
\(H_{1}: \mu > 31\)

Answer 2

The question involves determining the appropriate formulation of hypotheses for a statistical test. The scenario describes a production manager claiming that the contents of a canned milk product are at least 31 ounces. The task is to test this claim based on sample data.

In hypothesis testing, we set up two hypotheses: the null hypothesis (\(H_0\)) and the alternative hypothesis (\(H_1\)). The null hypothesis typically represents the status quo or a statement to be tested, while the alternative hypothesis represents what we want to prove or what we suspect is true.

1. \(H_0: \mu = 31\) and \(H_1: \mu > 31\): This set of hypotheses tests whether the mean is greater than 31, but it does not align with the manager's claim that the mean is at least 31.

2. \(H_0: \mu \leq 31\) and \(H_1: \mu > 31\): This is the correct formulation. The null hypothesis represents the opposite of the manager's claim (that the mean is less than or equal to 31), and the alternative hypothesis represents the manager's claim (that the mean is greater than 31).

3. \(H_0: \mu \geq 31\) and \(H_1: \mu < 31\): This set of hypotheses is testing the opposite of what we want to test. It is checking if the mean is less than 31, which is not the focus of the manager's claim.

4. \(H_0: \mu = 31\) and \(H_1: \mu = 31\): This is not a valid set of hypotheses since both hypotheses cannot be the same. The alternative hypothesis must be something different from the null hypothesis.

Therefore, the correct formulation of the hypotheses to test the manager's claim is \(H_0: \mu \leq 31\) and \(H_1: \mu > 31\).

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