Question

Q 3. For constructing a parkway (no trucks allowed), engineers need weights of cars for which the parkway is to be designed, to ensure a safe road. A simple random sample of 32 cars yields a mean of 3605.3 lb (pounds) with a standard deviation of 501.7 lb. Use a 0.01 significance level to test the claim that mean weight of cars is less than 3700 lb.

Q 4. From the data in Q 3, use a 0.01 significance level to test the claim that the standard deviation of weights of cars is less than 520 lb

Answer 1

Q3.

$\small \mu$ : Mean weight of the cars

$\small \mu_{o}$ : Hypothesized mean = 3700

Null hypothesis : H_o : $\small \mu$ = 3700 ; $\small \mu$ = $\small \mu_{o}$

Alternate hypothesis : H₁ : $\small \mu$ < 3700 ; $\small \mu$ < $\small \mu_{o}$

Left Tailed test

Test Statistic: tstat=x_Ho

Given
Hypothesized Mean : $\small \mu _{o}$	3700
Sample Mean : $\small \overline{x}$ : Sample mean weight of the cars	3605.3
Sample Standard Deviation : s: Sample standard deviation of weight of the cars	501.7
Sample Size : n: Number of randomly selected cars in the sample	32
Level of significance : $\small \alpha$	0.01
Degrees of Freedom : n-1	31

3605.3-3700)--94.7 =-1.0678 ( r-μο ー886889 Test Statistic: tstat sn501.7/V3266

For left tailed test :

P-Valte = P(t < tstat-Plt <-1.0678) = 0.1469

As P-Value i.e. is greater than Level of significance i.e (P-value:0.1469 > 0.01:Level of significance); Fail to Reject Null Hypothesis
There is not sufficient evidence to conclude that the mean weight of cars is less than 3700

Q4.

$\small \sigma$ :Standard deviation of the weight of the cars

$\small \sigma _{o}$ : hypothesized standard deviation = 520

Null hypothesis : $\small \sigma$ = 520 ; $\small \sigma$ = $\small \sigma _{o}$

Alternate hypothesis : H₁: $\small \sigma$ < 520; $\small \sigma$ < $\small \sigma _{o}$

Left tailed test

2(n 1)s2 Test Statistic: Xstat2

(32-1)×501.72 520 7802789.59 270400 28.8565

Test Statistic = 28.8565

Degrees of freedom = n-1 = 32-1 = 31

For left tailed test:

P - Value P< tstat) Ph228.8565) 0.4233

As P-Value i.e. is greater than Level of significance i.e (P-value:0.4233 > 0.05:Level of significance); Fail to Reject Null Hypothesis
There is not sufficient evidence to conclude that the standard deviation of weight of cars is less than 520 lb