Question

Part 1: Create your own Hypothesis Test and Confidence Interval from 1 sample Using methods from chapter 8, test ONE claim about a population parameter by collecting your own data or using our class survey data. Include your written claim, hypothesis in both symbolic and written form, relevant statistics (such as sample means, proportions etc.), test statistic, p-value (or critical value), conclusion, and interpretation of your conclusion in the context of your claim. Use a 0.05 significance level. You will also construct a 95% confidence interval estimate of your population parameter tested above and write a brief statement about how the interval validates or invalidates the claim you tested. Examples of potential Hypotheses: • Test the claim that the proportion of brown M&Ms in a minibag of candies is 5%. • Test the claim the proportion of your friends on Facebook who post something everyday is less than 42%. • Test the claim that the mean pulse rate of a person is less 75 beats per minute. • Test the claim that the mean wait time in line at your favorite coffee shop is greater than 2 minutes.

Answer 1

One sample t test

Lets test to see the mean pulse rate is 75 beats per second.

Say we take a sample of 100 members and get the sample mean as 74.5, SD=3

$t^*=\frac{74.5-75}{3/\sqrt{100}}=-1.666$

pvalue=P(t<-1.666)=0.0477

At 5% significance level, critical t stat=-1.645,

Hence we reject H0 and say the number os beats is less than 75.

$CI=74.5\pm1.645*\frac{3}{\sqrt{100}}=[74.0065, 74.9935 ]$

Paired t test

Lets take the test of apps on husband and wife phones

Lets say on an average there were 2.5 apps more in wifes phone with the SD of the difference being 3 among the 20 couples surveyed.

$t^*=\frac{2.5}{3/\sqrt{20}}=3.726$

pvalue=P(t>3.726,18dof)=0.0008

As pvalue<0.05, we reject H0 and say on an average women have more apps than men.

$CI=2.5\pm1.96*\frac{3}{\sqrt{20}}=[1.1852, 3.8148]$