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.
