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The subjects were assigned to the two treatment groups at random so that the groups were as similar as possible before the treatments.

This is necessary because otherwise, we would not be able to tell whether the differences observed after the treatments are due to the treatments themselves or to differences between the groups that existed prior to the treatments.

$$\begin{gathered} {\stackrel{¯}{x}}_1=19.883 \\ {\stackrel{¯}{x}}_2=15.739 \end{gathered}$$

The claim is that the intrinsic group has a higher mean creativity rating.

Either a null hypothesis or an alternative hypothesis is asserted.

$$\begin{gathered} H_0:{\mathrm{μ}}_1={\mathrm{μ}}_2 \\ {H}_0:{\mathrm{μ}}_1>{\mathrm{μ}}_2 \end{gathered}$$

Where,

${\mathrm{μ}}_1=$true mean creativity rating for the Intrinsic group.

${\mathrm{μ}}_2=$true mean creativity rating for the Extrinsic group.

As a result, the difference in sample means is,

$$\begin{gathered} {\stackrel{¯}{x}}_1-{\stackrel{¯}{x}}_2=19.883-15.739 \\ =4.144 \end{gathered}$$

When the null hypothesis is true, the $P$-value is the probability of getting the sample results or more extreme results.

Therefore, we note that $1$of the $100$dots lies to the right of $4.144$then, we have,

$$\begin{gathered} P-value=\frac{1}{100} \\ =0.01 \\ =1\% \end{gathered}$$

Therefore, when there is no difference in the mean creativity rating of intrinsic rewards and the mean creativity rating of extrinsic rewards, we conclude that there is a $1\%$ chance of getting similar sample results or more extreme results.

From part (b) we have,

we note that 1 of the 100 dots lies to the right of $4.144$then, we have,

$P-value=1\%$

And we know that the null hypothesis is rejected if the P-value is less than or equal to the significance level.

$P<0.05⇒\text{Reject}{H}_0$

Therefore, we conclude that the claim that intrinsic rewards promote creativity more than extrinsic rewards is supported by compelling evidence.

Part (c) of our conclusion states, "There is compelling evidence to support the claim that intrinsic rewards promote creativity more than extrinsic rewards."

When we reject a null hypothesis when the null hypothesis is true, we make a type I error. When we fail to reject the null hypothesis when the null hypothesis is false, we make a Type II error.

As a result, if we reject the null hypothesis, we have made a Type I error.