Questions: When you get a surprisingly low price on a product do you assume that you got a really good deal or that you bought a low-quality product? Research indicates that you are more likely to associate low price and low quality if someone else makes the purchase rather than yourself (Yan Sengupta, 2011). In a similar study, n=16 participants were asked to rate the quality of low-priced items under two scenarios: purchased by a friend or purchased yourself. The results produced a mean difference of M0=2.6 and SS=135, with self-purchases rated higher. Is the judged quality of objects significantly different for self-purchases than for purchases made by others? Use a two-tailed test with a=.05. Record your test results in the blanks below. estimated standard error is sMD= (round your answer to 2 decimal places, #.##) A) critical t values are t= ± (include 3 decimal places, #.###)

When you get a surprisingly low price on a product do you assume that you got a really good deal or that you bought a low-quality product? Research indicates that you are more likely to associate low price and low quality if someone else makes the purchase rather than yourself (Yan Sengupta, 2011). In a similar study, n=16 participants were asked to rate the quality of low-priced items under two scenarios: purchased by a friend or purchased yourself. The results produced a mean difference of M0=2.6 and SS=135, with self-purchases rated higher.

Is the judged quality of objects significantly different for self-purchases than for purchases made by others? Use a two-tailed test with a=.05. Record your test results in the blanks below.
estimated standard error is sMD= (round your answer to 2 decimal places, #.##)
A) critical t values are t= ± (include 3 decimal places, #.###)

Transcript text: When you get a surprisingly low price on a product do you assume that you got a really good deal or that you bought a low-quality product? Research indicates that you are more likely to associate low price and low quality if someone else makes the purchase rather than yourself (Yan \& Sengupta, 2011). In a similar study, $n=16$ participants were asked to rate the quality of low-priced items under two scenarios: purchased by a friend or purchased yourself. The results produced a mean difference of $M_{0}=2.6$ and $S S=135$, with self-purchases rated higher. Is the judged quality of objects significantly different for self-purchases than for purchases made by others? Use a two-tailed test with $a=.05$. Record your test results in the blanks below. estimated standard error is $s_{M D}=$ (round your answer to 2 decimal places, \#.\#\#) $\square$ A) critical $t$ values are $t= \pm$ (include 3 decimal places, \#.\#\#\#) $\square$ A

Solution

Solution Steps

Step 1: Calculate the Estimated Standard Error

The estimated standard error of the mean difference ($s_{M_D}$) is calculated using the formula:

\[ s_{M_D} = \frac{s}{\sqrt{n}} \]

where $s$ is the sample standard deviation and $n$ is the sample size. Given that the sum of squares ($SS$) is 135 and the sample size $n = 16$, we first compute the sample standard deviation:

\[ s = \sqrt{\frac{SS}{n - 1}} = \sqrt{\frac{135}{15}} = \sqrt{9} = 3 \]

Now, substituting $s$ into the formula for $s_{M_D}$:

\[ s_{M_D} = \frac{3}{\sqrt{16}} = \frac{3}{4} = 0.75 \]

Step 2: Calculate the t-statistic

The t-statistic is calculated using the formula:

\[ t = \frac{M_D}{s_{M_D}} \]

where $M_D$ is the mean difference. Given $M_D = 2.6$:

\[ t = \frac{2.6}{0.75} \approx 3.4667 \]

Step 3: Determine the Critical t-values

For a two-tailed test with a significance level of $\alpha = 0.05$ and degrees of freedom $df = n - 1 = 15$, we find the critical t-values using the t-distribution:

\[ t_{critical} = \pm t_{0.025, 15} \approx \pm 2.131 \]

Step 4: Decision on the Null Hypothesis

We compare the absolute value of the t-statistic to the critical t-values:

\[ |t| = 3.4667 > 2.131 \]

Since the t-statistic exceeds the critical value, we reject the null hypothesis.

Final Answer

The estimated standard error is $s_{M_D} = 0.75$, the critical t-values are $t = \pm 2.131$, and we reject the null hypothesis, indicating that the judged quality of objects is significantly different for self-purchases than for purchases made by others.

\[ \boxed{s_{M_D} = 0.75, \quad t = \pm 2.131, \quad \text{Reject the null hypothesis}} \]

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