Question

Researchers wanted to know if people, on average, tend to underestimate the duration of a typical cold. Clinical literature reports that the actual duration of a typical cold is roughly 15 days. The researchers surveyed a random sample of 352 healthy adults and asked them how long they think that a typical cold lasts. The results of this survey were that the average time that the 352 people thought a cold lasts was two weeks (14 days) with a standard deviation of 0.5 days. So, according to this survey, do people tend to underestimate the duration of a cold (with statistical significance)?

Answer 1

Answer:

No, the survey doesn't support the researchers claim that people tend to underestimate the duration of a cold. .

Step-by-step explanation:

We are given;

Population mean; μ = 15

Sample mean; x¯ = 14

Standard deviation; s = 0.5

Sample size; n = 352

Null hypothesis; H0: μ = 15

Alternative hypothesis; Ha: μ < 15

Let's find the z-value;

z = (x¯ - μ)/(s/√n)

z = (14 - 15)/(0.5/√352)

z = -1/0.02665

z = -37.5

From online p-value from z-score calculator attached using z = -37.5; significance level of 0.05; one tailed hypothesis, we have;

p-value = 0.00001

But since we want to find out if they underestimate the duration of the cold then;

P(z > 0.00001) = 1 - 0.00001 = 0.99999

Which is approximately 1.

The p-value is greater than the significance level, therefore we fail to reject the null hypothesis and conclude that the survey doesn't support the researchers claim that people tend to underestimate the duration of a cold.