Question

Question 7 An online tutoring service claims that students who take their ACT preparation course have a mean ACT score of at least 25.8. A consumer advocate is suspicious of this claim. The advocate polls 32 students who used the service. The students in the sample had a mean ACT score of 24.9, with a standard deviation of 3.8. Test for evidence that the mean ACT score for people using this service is actually lower than 25.8. Use a level of significance of a = 0.10. O p = 0.1901 We reject the null hypothesis. There is sufficient evidence at the 10% level of significance to suggest that the mean ACT score for people using this service is less than 25.8. O p = 0.1901 We do not reject the null hypothesis. There is not sufficient evidence at the 10% level of significance to suggest that the mean ACT score for people using this service is less than 25.8. O p = 0.0902 We reject the null hypothesis. There is sufficient evidence at the 10% level of significance to suggest that the mean ACT score for people using this service is less than 25.8. O p = 0.0950 We do not reject the null hypothesis. There is not sufficient evidence at the 10% level of significance to suggest that the mean ACT score for people using this service is less than 25.8. p = 0.0950 O We reject the null hypothesis. There is sufficient evidence at the 10% level of significance to suggest that the mean ACT score for people using this service is less than 25.8. O p = 0.0902 We do not reject the null hypothesis. There is not sufficient evidence at the 10% level of significance to suggest that the mean ACT score for people using this service is less than 25.8.

Answer 1

H0: $\mu$ >= 25.8 ,

Ha: $\mu$ < 25.8

Test statistics

t = ( $\bar{x}$ - $\mu$ ) / ( S / sqrt( n) )

= ( 24.9 - 25.8) / ( 3.8 / sqrt(32 ) )

= -1.34

df = n - 1 = 32 - 1 = 31

From T table,

With test statistics of 1.34 and df of 31,

p-value = 0.0950

Since p-value < 0.10 level, reject H0.

p= 0.0950

We reject the null hypothesis. There is sufficient evidence at 10% level of significance to suggest that

The mean ACT score for the people using his service is less than 25.8