A sociologist studying fertility in France and Switzerland wanted to test if there was a difference in the average number of babies women in each country have. The sociologist obtained a random sample of women from each country. Here are the results of their test:
\begin{tabular}{lrrrr}
& \multicolumn{2}{c}{ \# of babies } & & \
Country & $n$ & Mean & StDev & SE mean \
\hline France & 100 & 1.85 & 1.3 & 0.13 \
Switzerland & 100 & 1.65 & 1.2 & 0.12 \
$\mathrm{t}$ test for $\mu_{\mathrm{F}}
eq \mu_{\mathrm{S}}$ & $t=1.13$ & $p=0.26$ & $\mathrm{DF}=197$ &
\end{tabular}

Assume that all conditions for inference have been met.
At the $\alpha=0.05$ level of significance, is there sufficient evidence to conclude that there is a difference in the average number of babies women in each country have?

Choose 1 answer:
(A) Yes, since the $\mathrm{P}$-value is greater than 0.05 .
(B) Yes, since the test statistic is greater than 0.05 .
(C) No, since the $P$-value is greater than 0.05 .
(D) No, since the test statistic is greater than 0.05 .

Question

A sociologist studying fertility in France and Switzerland wanted to test if there was a difference in the average number of babies women in each country have. The sociologist obtained a random sample of women from each country. Here are the results of their test:
\begin{tabular}{lrrrr} 
& \multicolumn{2}{c}{ \# of babies } & & \
Country & $n$ & Mean & StDev & SE mean \
\hline France & 100 & 1.85 & 1.3 & 0.13 \
Switzerland & 100 & 1.65 & 1.2 & 0.12 \
$\mathrm{t}$ test for $\mu_{\mathrm{F}} 
eq \mu_{\mathrm{S}}$ & $t=1.13$ & $p=0.26$ & $\mathrm{DF}=197$ &
\end{tabular}

Assume that all conditions for inference have been met.
At the $\alpha=0.05$ level of significance, is there sufficient evidence to conclude that there is a difference in the average number of babies women in each country have?

Choose 1 answer:
(A) Yes, since the $\mathrm{P}$-value is greater than 0.05 .
(B) Yes, since the test statistic is greater than 0.05 .
(C) No, since the $P$-value is greater than 0.05 .
(D) No, since the test statistic is greater than 0.05 .

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Determine the significance level for the hypothesis test. ‖ ‖ step 2 ⋮ Compare the p-value to the significance level. ‖ ‖ step 3 ⋮ Make a decision based on the comparison. If the p-value is less than or equal to the significance level, reject the null hypothesis. If the p-value is greater than the significance level, fail to reject the null hypothesis. ‖ ‖ step 4 ⋮ Apply this decision rule to the given p-value of 0.26 and the significance level of 0.05. ‖ ‖ step 5 ⋮ Since the p-value (0.26) is greater than the significance level (0.05), we fail to reject the null hypothesis. ‖ ***C*** ∻Key Concept∻ ⚹Hypothesis Testing and P-value⚹ ∻Explanation∻ ⚹In hypothesis testing, if the p-value is greater than the significance level (α), there is not enough evidence to reject the null hypothesis.⚹◊What is the formula for calculating the t-test statistic in hypothesis testing given the sample data and results provided?⍭ Generate me a similar question◊

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