Question

1) For each situation, state the null and alternative hypotheses: (Type "mu" for the symbol ?μ , e.g.  mu >1 for the mean is greater than 1, mu < 1 for the mean is less than 1, mu not = 1 for the mean is not equal to 1. Please do not include units such as "mm" or "$" in your answer.)

(a) The diameter of a spindle in a small motor is supposed to be 5.7 millimeters (mm) with a standard deviation of 0.13 mm. If the spindle is either too small or too large, the motor will not work properly. The manufacturer measures the diameter in a sample of 13 spindles to determine whether the mean diameter has moved away from the required measurement. Suppose the sample has an average diameter of 5.77 mm.
?0:  
??:

(b) Harry thinks that prices in Caldwell are lower than the rest of the country. He reads that the nationwide average price of a certain brand of laundry detergent is $23.65 with standard deviation $1.57. He takes a sample from 4 local Caldwell stores and finds the average price for this same brand of detergent is $24.91.
?0 :
??:

2) Traffic police monitor the speed of vehicles as they travel over a new bridge. The average speed for a sample of 31 vehicles was 82.72km/h, with the sample standard deviation being 4.61 km/h. We will assume that the speeds are Normally distributed, and the police are interested in the mean speed.

Part a) Since the variance of the underlying Normal distribution is not known, inference here would involve the t distribution. How many degrees of freedom would the relevant t distribution have?

Part b) Create a 95 % confidence interval for the mean speed of vehicles crossing the bridge. Give the upper and lower bounds to your interval, each to 2 decimal places. ( ... , ....)

3) Ben thinks that people living in a rural environment have a healthier lifestyle than other people. He believes the average lifespan in the USA is 77 years. A random sample of 9 obituaries from newspapers from rural towns in Idaho give ?¯=80.32 and ?=0.73  Does this sample provide evidence that people living in rural Idaho communities live longer than 77 years?

(a) State the null and alternative hypotheses: (Type "mu" for the symbol μ , e.g.  mu >1 for the mean is greater than 1,  mu < 1 for the mean is less than 1, mu not = 1 for the mean is not equal to 1)
?0 :  
??:

(b) Find the test statistic, t =

Answer 1

Que.1

Part a .

Part b .

Que.2

2) Traffic police monitor the speed of vehicles as they travel over a new bridge. The average speed for a sample of 31 vehicles was 82.72km/h, with the sample standard deviation being 4.61 km/h. We will assume that the speeds are Normally distributed, and the police are interested in the mean speed.

n = 31

S = 4.61

part a.

Degrees of freedom = df = n-1 = 31-1 = 30

df = 30

Part b .

Confidence interval for 95%

Using T table critical value for 95% confidence at 30 df

tc = 2.042

confidence interval formula

95 % confidence interval for the mean speed of vehicles crossing the bridge is ( 81.03, 84.41)

Que. 3

Ben thinks that people living in a rural environment have a healthier lifestyle than other people. He believes the average lifespan in the USA is 77 years. A random sample of 9 obituaries from newspapers from rural towns in Idaho give ?¯=80.32 and ?=0.73  Does this sample provide evidence that people living in rural Idaho communities live longer than 77 years?

(a) State the null and alternative hypotheses:

b . test statistics