Question

Lexie, a bowler, claims that her bowling score is more than 140 points, on average. Several of her teammates do not believe her, so she decides to do a hypothesis test, at a 5% significance level, to persuade them. She bowls 18 games. The mean score of the sample games is 155 points. Lexie knows from experience that the standard deviation for her bowling score is 17 points. H0: μ=140; Ha: μ>140 α=0.05 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?

Answer 1

The test statistic is
`t = 3.744`

Explanation:

From the question we are told that

The population mean is
`\mu = 140`

The The level of significance is
`\alpha = 0.05`

The sample size is n = 18

The null hypothesis is
`H_o : \mu = 140`

The alternative hypothesis is
`H_a : \mu > 140`

The sample mean is
`\= x = 155`

The standard deviation is
`\sigma = 17`

Generally the test statistics is mathematically represented as

`t = (\= x - \mu )/( ( \sigma)/( √(n) ) )`

substituting values

`t = ( 155 - 140 )/( ( 17 )/( √(18) ) )`

`t = 3.744`