Math  /  Data & Statistics

QuestionTwo of the hottest smartphones on the market are the newly released iPhone6 and the Samsung Galaxy S6. CNet.com offers online reviews of all major cell phones, including battery life tests. In a review of the iPhone6, the talk-time battery life of 35 iPhones was measured. Similarly, the talk-time battery life of 30 Galaxy S6s was measured.
Two outputs are given below. Which is appropriate for analyzing the data collected? ``` Output 1 Hhi Mean of iPhone6 \muz: Mean of Galaxy S6 ``` \begin{tabular}{|l|c|c|} \hline Difference & Sample Diff. & Std. Err. \\ \hlineμ1μ2\mu_{1}-\mu_{2} & -0.71759861 & 0.189403 \\ \hline \end{tabular}
Possible p-values: 0.0001,0.0002,0.99990.0001,0.0002,0.9999 Output 2 HR=mH_{R}=\mathrm{m} ean of the paired difference between iPhone6 and Galaxy 56 \begin{tabular}{|c|c|c|} \hline Difference & Sample Diff. & Std. Err. \\ \hline iPhone6 - Galaxy S6 & -0.754246 & 0.192151 \\ \hline \end{tabular}
Possible p-values: 0.0002,0.0004,0.99980.0002,0.0004,0.9998 Output 1 Output 2
Using the StatCrunch output chosen above, determine if there is a difference in the mean battery life for the two phones. Use a significance level of 0.01 when conducting the test. - Select the appropriate hypotheses. Make sure the notation used in the hypotheses agrees with the type of samples selected in the output. Ho:μd=0Ho:μd=0Ho:μd=0Ho:μ1=μ2Ho:μ1=μ2Ho:μ1=μ2Ha:μd>0Ha:μd<0Ha:μd0Ha:μ1<μ2Ha:μ1>μ2Ha:μ1μ2\begin{array}{llllll} H_{o}: \mu_{d}=0 & H_{o}: \mu_{d}=0 & H_{o}: \mu_{d}=0 & H_{o}: \mu_{1}=\mu_{2} & H_{o}: \mu_{1}=\mu_{2} \quad H_{o}: \mu_{1}=\mu_{2} \\ H_{a}: \mu_{d}>0 & H_{a}: \mu_{d}<0 & H_{a}: \mu_{d} \neq 0 & H_{a}: \mu_{1}<\mu_{2} & H_{a}: \mu_{1}>\mu_{2} & H_{a}: \mu_{1} \neq \mu_{2} \end{array} - α=\alpha= \square reject HoH_{o} if probability \square α\alpha - TS:t=\mathrm{TS}: \mathrm{t}= \square (make sure you reference the probabilities in the output you selected in the - probability = ) first question) - decision: Select an answer (6) - At the 0.01 level, there Select an answer significant evidence to conclude the mean battery life for an iPhone 6 is Select an answer (0) than the mean for a Galaxy S6.

Studdy Solution

STEP 1

1. We are comparing the mean battery life of two independent groups: iPhone6 and Galaxy S6.
2. The data collected involves independent samples, not paired samples.
3. We are using a significance level (α\alpha) of 0.01.

STEP 2

1. Select the appropriate output for analysis.
2. Formulate the hypotheses based on the selected output.
3. Conduct the hypothesis test using the selected output.
4. Make a decision based on the test results.

STEP 3

Identify the correct output for independent samples.
Output 1 is appropriate because it compares the mean of two independent groups (μ1\mu_1 and μ2\mu_2).

STEP 4

Formulate the hypotheses for independent samples:
- Null Hypothesis (H0H_0): μ1=μ2\mu_1 = \mu_2 - Alternative Hypothesis (HaH_a): μ1μ2\mu_1 \neq \mu_2

STEP 5

Conduct the hypothesis test:
- Given: Sample Difference = -0.71759861, Std. Err. = 0.189403 - Possible p-values: 0.0001, 0.0002, 0.9999
Since we are testing μ1μ2\mu_1 \neq \mu_2, we look for a two-tailed p-value. The smallest p-value is 0.0001.

STEP 6

Make a decision:
- α=0.01\alpha = 0.01 - Since the p-value (0.0001) is less than α\alpha, we reject H0H_0.
Decision: There is significant evidence at the 0.01 level to conclude that the mean battery life for an iPhone 6 is different from the mean for a Galaxy S6.

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