Question

Golf-course designers have become concerned that old courses are becoming obsolete since new technology has given golfers the ability to hit the ball so far. Designers, therefore, have proposed that new golf courses need to be built expecting that the average golfer can hit the ball more than 235 yards on average. Suppose a random sample of 102 golfers be chosen so that their mean driving distance is 9 yards. The population standard deviation is 41.7. Use a 5% significance level. (round your answer to four decimal places)

Calculate the followings for a hypothesis test where H0:μ=235 H1:μ<235

The test statistic is:

The P-value is:

Answer 1

Here, we have to use one sample z test for the population mean.

The null and alternative hypotheses are given as below:

H0: µ = 235 versus Ha: µ < 235

This is a lower tailed test.

The test statistic formula is given as below:

Z = (x̄ - µ)/[σ/sqrt(n)]

From given data, we have

µ = 235

x̄ = 9

σ = 41.7

n = 102

α = 0.05

Critical value = -1.6449

(by using z-table or excel)

Z = (9 - 235)/[41.7/sqrt(102)]

Z = -54.7359

Test statistic = -54.7359

P-value = 0.0000

(by using Z-table)

P-value < α = 0.05

So, we reject the null hypothesis