Browsing on the mobile device.

Browsing on the mobile device.#

A survey of 1620 American adults indicates that 39.0% of cell phone owners browse the internet exclusively on their phone rather than a computer or other device. According to an online article, a report from a mobile research company indicates that 38% of Chinese mobile web users only access the internet through their cell phones. Conduct a hypothesis test to determine if these data provide strong evidence that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%.

Part 1: (a)#

Formulate the null and alternative hypothesis.

Answer Section#

  • \(H_0: p = 0.39\), \(H_A: p ≠ 0.38\)

  • \(H_0: p = 0.39\), \(H_A: p = 0.38\)

  • \(H_0: p = 0.38\), \(H_A: p ≠ 0.38\)

  • \(H_0: p ≠ 0.38\), \(H_A: p = 0.38\)

Part 1: (b)#

Calculate the test statistic (Z) for the hypothesis test using the provided information.

Answer Section#

Please enter in a numeric value.

Part 1: (c)#

Determine the p-value from the calculated test statistic.

Answer Section#

Please enter in a numeric value.

Part 1: (d)#

Based on the p-value and a significance level of 0.05, state whether you will reject or fail to reject the null hypothesis and explain the conclusion.

Answer Section#

  • As the p-value is less than 0.05, we reject \(H_0\), then the data provide strong evidence that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%, and the data indicate that the proportion is lower in the US.

  • As the p-value is greater than or equal to 0.05, we fail to reject \(H_0\), then the data does not provide strong evidence to show that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%.

Part 2: (a)#

Calculate the lower bound of a 95% confidence interval for the proportion of Americans who access the internet on their cell phones.

Answer Section#

Please enter in a numeric value in.

Part 2: (b)#

Calculate the upper bound a 95% confidence interval for the proportion of Americans who access the internet on their cell phones.

Answer Section#

Please enter in a numeric value in.

Part 2: (c)#

Interpret the interval in this context.

Answer Section#

  • We are 95% confident that approximately [Lower bound] to [Upper bound] of all Americans primarily use their cell phones to browse the internet.

  • We are 90% confident that [Lower bound] to [Upper bound] of all Americans primarily use their cell phones to browse the internet, but this range could also be 10% to 30%.

  • We are 99% confident that [Lower bound] to [Upper bound] of all Americans always use their cell phones to browse the internet, with no variability.

Attribution#

Problem is from the OpenIntro Statistics textbook, licensed under the CC-BY 4.0 license.
Image representing the Creative Commons 4.0 BY license.