Questions: For a one-tailed hypothesis test where you reject H0 only in the lower tail, the critical value is -1.3253. What is the statistical decision if tSTAT = -1.64? What is the statistical decision? A. Since the tSTAT value is less than the critical value, do not reject H0. B. Since the tSTAT value is greater than or equal to the critical value, reject H0. C. Since the tSTAT value is less than the critical value, reject H0. D. Since the tSTAT value is greater than or equal to the critical value, do not reject H0.

For a one-tailed hypothesis test where you reject H0 only in the lower tail, the critical value is -1.3253. What is the statistical decision if tSTAT = -1.64? What is the statistical decision? A. Since the tSTAT value is less than the critical value, do not reject H0. B. Since the tSTAT value is greater than or equal to the critical value, reject H0. C. Since the tSTAT value is less than the critical value, reject H0. D. Since the tSTAT value is greater than or equal to the critical value, do not reject H0.
Transcript text: For a one-tailed hypothesis test where you reject $\mathrm{H}_{0}$ only in the lower tail, the critical value is -1.3253 What is the statistical decision if $\mathrm{t}_{\text {STAT }}=-1.64$ ? What is the statistical decision? A. Since the $\mathrm{t}_{\text {STAT }}$ value is less than the critical value, do not reject $\mathrm{H}_{0}$. B. Since the $\mathrm{t}_{\text {STAT }}$ value is greater than or equal to the critical value, reject $\mathrm{H}_{0}$. C. Since the $\mathrm{t}_{\text {STAT }}$ value is less than the critical value, reject $\mathrm{H}_{0}$ D. Since the $\mathrm{t}_{\text {STAT }}$ value is greater than or equal to the critical value, do not reject $\mathrm{H}_{0}$
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Solution

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To determine the statistical decision, compare the given t-statistic value with the critical value. If the t-statistic is less than the critical value, reject the null hypothesis \( \mathrm{H}_{0} \). Otherwise, do not reject \( \mathrm{H}_{0} \).

Schritt 1: Gegebene Werte identifizieren

Die gegebenen Werte sind:

  • \( t_{\text{STAT}} = -1.64 \)
  • Kritischer Wert = -1.3253
Schritt 2: Vergleich der Werte

Vergleiche den \( t_{\text{STAT}} \)-Wert mit dem kritischen Wert:

  • Wenn \( t_{\text{STAT}} < \) kritischer Wert, dann lehne \( H_0 \) ab.
  • Andernfalls lehne \( H_0 \) nicht ab.
Schritt 3: Entscheidung treffen

Da \( t_{\text{STAT}} = -1.64 \) kleiner ist als der kritische Wert von -1.3253, lehnen wir \( H_0 \) ab.

Endgültige Antwort

Die Antwort ist C: Da der \( t_{\text{STAT}} \)-Wert kleiner ist als der kritische Wert, lehnen wir \( H_0 \) ab.

\(\boxed{\text{C}}\)

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