Question

Does the use of fancy type fonts slow down the reading of text on a computer screen? Adults can read four paragraphs of text in the common Times New Roman font in an average time of 22 seconds. Researchers asked a random sample of 24 adults to read this text in the ornate font named Gigi. Here are their times, in seconds: 23.2, 21.2, 28.9, 27.7, 29.1, 27.3, 16.1, 22.6, 25.6, 34.2, 23.9, 26.8, 20.5, 34.3, 21.4, 32.6, 26.2, 34.1, 31.5, 24.6, 23.0, 28.6, 24.4, 28.1

To know whether it takes more time to read text in this ornate font, conduct a hypothesis test for the hypothesis H0: µ = 22 against Ha: µ > 22. Report the t-statistic with degrees of freedom, and give (a range for) the P-value.

Answer 1

From the above data, let's find out the mean and standard deviation as follows.

where Variance = Sum of squared differences/ (n-1) = 514.05/(24-1) = 22.35

Standard Deviation = Variance = 22.35 = 4.7276

Number of samples (n) = 24

Hence standard error of sample means = SD of sample/ n = 4.7276/ 24 = 0.9650

Let's now discuss about the hypothesis.

Null Hypothesis (H0) : µ 22

Alternate Hypothesis (Ha): µ > 22

Degrees of Freedom = n-1 = 24-1 = 23

t statistics = (sample mean - µ₀)/ standard error = (26.4958-22)/0.9650 = 4.6588

Please note, the above test is a one tailed test as we are trying to analyse if the mean is greater than 22 or not.

Let's assume a significance level of 5%.

At 5% significance level and DF of 23, the critical t statistics from the one tailed distribution is 1.714.

As it's a one tailed test, we can reject the null hypothesis if t statistics > 1.714

As t statistics calculated is 4.6588 which is greater than the critical value of 1.714, we can safely reject the null hypothesis.

Hence we can say that the population mean (average time to read ornate font) is more than 22 seconds.

P value for a t statistics of 4.6588 with 23 degrees of freedom is 0.00005.