Question

TaxiCab held 20% of the rides last year. A random sample of 100 rides this year showed that 25 employed TaxiCab. Has the percentage of TaxiCab rides increased this year compared to last year? Formulate the hypothesis:

A. Ho: p≤.25 . Ha: p>.25

B. Ho: p≤.20 . Ha: p>.20

C. Ho: p<.25 . Ha: p>.25

D. Ho: p>.20 . Ha: p≤.20

What is the p-value?

What is your conclusion with 95% confidence?

Answer 1

Here given that  A random sample of 100 rides this year showed that 25 employed TaxiCab

So Porportion of candies that are blue , = 25/100 = 0.25

Sample size, n = 100

Here we need to test whether percentage of TaxiCab rides increased this year compared to last year or not

TaxiCab held 20% of the rides last year

Question (a)

Null Hypothesis H₀: p 0.2

Alternate Hypothesis H₁ : p 0.2

So Answer is Option B

Null Hypothesis value, p₀ = 0.2

Question (b)

Z-test statistic = ( -  p₀ ) / p₀ * ( 1 - p₀ ) / n

= (0.25 - 0.2) / 0.2 * (1 - 0.2) / 100

= 0.05 /  0.0016

= 0.05 / 0.04

= 1.25

So test statistic for this hypothesis test = 1.25

The p-value for a z-test statistic of 1.25 for a right-tailed test = 0.1056498 from online calculator

= 0.1056 rounded to 4 decimal places

Question (c)

Here confidence level = 95% = 0.95

Significance level = 1 - 0.95 = 0.05

Since the p-value is not less than the significance level, we fail to reject Null Hypothesis H₀. There is not enough evidence to support the claim that the  percentage of TaxiCab rides increased this year compared to last year