The "think tank" should update their estimate of the typical number of text messages sent per day by a teenager to a number greater than 50.
We can use a one-sample t-test to determine whether the mean number of text messages sent per day by a typical teenager is greater than 50. The null hypothesis is that the mean number of text messages is equal to 50, and the alternative hypothesis is that the mean number of text messages is greater than 50.
The t-statistic is calculated as follows:
t = (mean - hypothesized mean) / (standard deviation / sqrt(n))
where:
mean is the sample mean
hypothesized mean is the hypothesized mean (in this case, 50)
standard deviation is the sample standard deviation
n is the sample size
The p-value is the probability of getting a test statistic as extreme or more extreme than the observed test statistic, assuming that the null hypothesis is true.
In this case, the mean number of text messages is 82.5, the standard deviation is 56.96, and the sample size is 12. The t-statistic is 1.98, and the p-value is 0.037.
Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that the mean number of text messages sent per day by a typical teenager is greater than 50.
In other words, there is sufficient evidence to say that the population mean number of text messages sent per day in by a typical teenager is more than 50.
Therefore, the "think tank" should update their estimate of the typical number of text messages sent per day by a teenager to a number greater than 50.
Question
3. A Washington, D. C., “think tank” announces the typical teenager sent 50 text messages per day in 2009. To update the estimate, you phone a sample of teenagers and ask them how many text messages they sent the previous day. Their responses were: 51 175 47 49 44 54 145 203 21 59 42 100 At 0.05 level, can you conclude that the mean number is greater than 50? Estimate the p-value and describe what it tells you. 4