Question

A report by the Gallup Poll found that a woman visits her doctor, on average, at most 5.8 times each year. A random sample of 20 women results in these yearly visit totals: 3; 2; 1; 3; 7; 2; 9; 4; 6; 6; 8; 0; 5; 6; 4; 2; 1; 3; 4; 1

At the alpha = 0:05 level, can it be concluded that the sample mean is higher than 5.8 visits per year? Find the p-value and explain how it can be used to make your conclusion (Assume the sample comes from the normal distribution).

Please use the t-table and explain or write all the steps

Answer 1

Solution: The null and alternative hypotheses are:

Under the null hypothesis, the test statistic is:

The mean and standard deviation of the given data is:

Conclusion: Since the p-value is greater than the significance level, we, therefore, fail to reject the null hypothesis and conclude that there is not sufficient evidence to conclude that the sample mean is higher than 5.8 visits per year.