Question

You wish to test the following claim (Hį) at a significance level of a = 0.10. Ho:= 86.7 H1: > 86.7 You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: 90.2 102 94.8 100.3 94.1 95.3 72.8 80.6 94.5 102.5 85.1 93.8 104.9 84. 8 89.5 96.8 86.2 95.8 83 81.1 80.2 74.4 82.6 81.1 98.9 90 93.4 98.6 | 83 83. 9 86.7 91.8 What is the critical value for this test? (Report answer accurate to three decimal places.) critical value = What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = The test statistic is... Cin the critical region not in the critical region
PLS answer both questions!!thank you so so so so much!!!

Answer 1

1)

As you do not know the population s.d we will use t distribution to estimate the test

Sample size n = 32

Degrees of freedom is = n-1 = 31

For degrees of freedom 31 and 0.1 alpha critical value t from t distribution is = 1.309

Critical value is = 1.309

Rejection region is

Reject Ho if test statistics is greater than 1.309

Test statistics t = (sample mean - claimed mean)/(s.d/√n)

That is we need to calculate the sample mean and s.d of the given data

Test statistics t = (89.7719 - 86.7)/(8.281/√32)

Test statistics = 2.09845315408 ~ 2.098

Yes test statistics is in critical region as 2.098 > 1.309

Reject Ho

2)

Here alpha = 0.1

N = 12

For 12 df and 0.1 alpha

Critical value t is = -1.363

Reject Ho if test statistics is less than -1.363

Test statistics = (51.1583 - 61.5)/(7.3034/√12)

Test statistics = −4.9052084882 ~ -4.905

Yes it is in critical region

As -4.905 < -1.363

Reject Ho