Question

1. Test the claim that the proportion of people who own cats is significantly different than 30% at the 0.2 significance level.
The null and alternative hypothesis would be:

a) H0:μ≤0.3
Ha:μ>0.3

b) H0:p≥0.3
Ha:p<0.3

c) H0:μ≥0.3
Ha:μ<0.3

d) H0:p≤0.3
Ha:p>0.3

e) H0:μ=0.3
Ha:μ≠0.3

f) H0:p=0.3
Ha:p≠0.3

The test is:

-left-tailed

-two-tailed

-right-tailed

Based on a sample of 400 people, 31% owned cats
The p-value is: ____? (to 2 decimals)

Based on this we:

• Reject the null hypothesis
• Fail to reject the null hypothesis

2. You wish to test the following claim (HaHa) at a significance level of α=0.01α=0.01.
      Ho:μ=89.7
      Ha:μ≠89.7
You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=12 with mean M=93.7 and a standard deviation of SD=8.6

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value = ______?
The p-value is...

• less than (or equal to) αα
• greater than αα

This p-value leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 89.7.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 89.7.
• The sample data support the claim that the population mean is not equal to 89.7.
• There is not sufficient sample evidence to support the claim that the population mean is not equal to 89.7.

Answer 1

1). The null and alternative hypothesis would be:

  H0: p=0.3
Ha: p≠0.3 (option F)

The test is: both-tailed

calculation of test statistic:-

p value = 0.66 (using minitab or p value calculator)

Based on this we: fail to Reject the null hypothesis

[ because p value = 0.66 >0.20,so we do not have enough evidence to reject our null hypothesis.]

2).hypothesis:

Ho:μ=89.7
Ha:μ≠89.7

given data:-

sample size (n)=12

mean (M) = 93.7

sample standard deviation(s) = 8.6

hypothesized mean (μ) =89.7

test statistic:-

df= (12-1) = 11

p value = 0.1355 (using p value calculator for t= 1.611, alpha=0.01. df=11,both tailed test)

The p-value is:- greater than α

This p-value leads to a decision:- fail to reject the null hypothesis.

the conclusion be:-

There is not sufficient sample evidence to support the claim that the population mean is not equal to 89.7.

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