Question

A poll done by the US Bureau of Labor Statistics found that the average cell phone bill in 2018 was $114 a month. A random sample of 50 people taken recently shows an average bill of $122 per month with a standard deviation of $18.50.

Is there statistically significant evidence that the mean cell phone bill in the US has risen since 2018? Carry out a hypothesis test with a significance level of 0.05. Make sure you check the necessary critera.

Answer 1

The test hypothesis is

This is a one-sided test because the alternative hypothesis is formulated to detect the difference from the hypothesized mean on the upper side
Now, the value of test static can be found out by following formula:

Since the sample size is n = 50, degrees of freedom on the t-test statistic are n-1 = 50-1 = 49
This implies that

Since , we reject the null hypothesis in favor of the alternative hypothesis .
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