Question

In a study of the accuracy of fast food​ drive-through orders, one restaurant had 39 orders that were not accurate among 327 orders observed. Use a 0.10 significance level to test the claim that the rate of inaccurate orders is equal to​ 10%. Does the accuracy rate appear to be​ acceptable? Identify the null and alternative hypotheses for this test. Choose the correct answer below. Identify the test statistic for this hypothesis test.

The test statistic for this hypothesis test is____ . ​(Round to two decimal places as​ needed.)

Identify the​ P-value for this hypothesis test.

The​ P-value for this hypothesis test is____

Please explain how to get the P-VALUE with a TI-84 PLUS or using the table. when I look at the table it equals .8770 what is the correct way to do this?

Answer 1

Solution :

Given that,

= 0.10

1 - = 0.90

n = 327

x = 39

Level of significance = = 0.10

Point estimate = sample proportion = = x / n = 0.119

This a two- tailed test.

The null and alternative hypothesis is,

Ho: p = 0.10

Ha: p 0.10

1)

Test statistics

z = ( - ) / *(1-) / n

= ( 0.119 - 0.10) / (0.10*0.90) / 327

= 1.16

2)

P-value = 2 * P(Z > z )

= 2 * ( 1 - P(Z < 1.16) )

= 2 * 0.123

= 0.2460