The instructions for this is To provide an appropriate response ) The mean utili

Question

The instructions for this is To provide an appropriate response ) The mean utility bill in one city during the summer was less than $107. Write the null and alternative The mean repair bill of cars is greater than $150. Write the null and alternative hypotheses The mean age of judges in Los Angeles is 56.3 years. Identify the type I and type Il ernors for the of this claim. bypothesis test A recent study claimed that at least 15% of junior high students are overweight ln a sample of 160 students, 18 were found to be overweight. At 005, test the dam An airline claims that the no-show rate for passengers is less than 5% In a sample of 420 randomly selected reservations, 19 were no-shows. At a = 0.01, test the airline's darn. Round P to the nearest thousandth when calculating the test statistic Use a t-test to test the claim u s 3.1 at a 005, given the sample statistics n-15,x-3.4, and s 0.3. Round the test statistic to the nearest thousandth. A local retailer claims that the mean waiting time is less than 5 minutes. A random sample of 20 waiting times has a mean of 3.4 minutes with a standard deviation of 2.1 minutes. At a-0.01, test the retailer's claim. Assume the distribution is normally distributed. Round the test statistic to the nearest thousandth. A manufacturer dlaims that the mean lifetime of its lithium batteries is 1100 hours A homeowner selects 25 of these batteries and finds the mean lifetime to be 1080 hours with a standard deviation of 80 hours. Test the manufacturer's claim Use = 0.05. Round the test statistic to the nearest thousandth.

Explanation / Answer

#1.
H0: mu = 107
H1: mu < 107 (claim is that mean utility bill during summer is less than 107)

#2.
H0: mu = 5150
H1: mu > 5150 (claim is that mean repair bill greater than 5150)

#3.
Type I error will occur when we reject the null hypothesis though the mean age of judges in lA is 56.3 years

Type II error will occur when we fail to reject the null hypothesis though the mean age of judges in LA is different that 56.3 years.

#4.
Below are the null and alternate hypothesis
H0: p = 0.15
H1: p < 0.15

pcap = 18/160 = 0.1125

Test statistics, z = (0.1125 - 0.15)/sqrt(0.15*0.85/180) = -1.409

p-value = 0.0794

As p-value is greater than the singnificance level of 0.05, we fail to reject the null hypothesis.

Hence there are not significant evidence to conclude that proportion is less than 0.15.

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